definition_height int64 0 59 ⌀ | is_auto_or_private bool 2
classes | is_internal_name bool 2
classes | kind stringclasses 7
values | module stringlengths 12 90 | name stringlengths 2 347 | namespace stringlengths 0 235 | reducibility stringclasses 3
values | statement_dag_size int64 1 13.9k | type_refs listlengths 0 229 | value_dag_size int64 1 95.1k ⌀ | value_refs listlengths 0 699 |
|---|---|---|---|---|---|---|---|---|---|---|---|
null | false | false | theorem | Mathlib.MeasureTheory.Measure.AEMeasurable | AEMeasurable.exists_measurable_nonneg | AEMeasurable | null | 137 | [
"AEMeasurable",
"And",
"Exists",
"Filter.Eventually",
"Filter.EventuallyEq",
"LE.le",
"Measurable",
"MeasurableSpace",
"MeasureTheory.Measure",
"MeasureTheory.Measure.instFunLike",
"MeasureTheory.Measure.instOuterMeasureClass",
"MeasureTheory.ae",
"OfNat.ofNat",
"Pi.hasLe",
"Pi.instZero"... | 520 | [
"AEMeasurable",
"AEMeasurable.exists_ae_eq_range_subset",
"And",
"And.casesOn",
"And.intro",
"Exists",
"Exists.casesOn",
"Exists.intro",
"Filter.Eventually",
"Filter.EventuallyEq",
"LE.le",
"Measurable",
"MeasurableSpace",
"MeasureTheory.Measure",
"MeasureTheory.Measure.instFunLike",
"... |
null | false | false | theorem | Mathlib.MeasureTheory.Function.SpecialFunctions.Basic | AEMeasurable.exp | AEMeasurable | null | 36 | [
"AEMeasurable",
"MeasurableSpace",
"MeasureTheory.Measure",
"Real",
"Real.exp",
"Real.measurableSpace"
] | 40 | [
"AEMeasurable",
"Measurable.comp_aemeasurable",
"MeasurableSpace",
"MeasureTheory.Measure",
"Real",
"Real.exp",
"Real.measurableSpace",
"Real.measurable_exp"
] |
null | false | false | theorem | Mathlib.MeasureTheory.Measure.AEMeasurable | AEMeasurable.fst | AEMeasurable | null | 59 | [
"AEMeasurable",
"MeasurableSpace",
"MeasureTheory.Measure",
"Prod",
"Prod.fst",
"Prod.instMeasurableSpace"
] | 72 | [
"AEMeasurable",
"Measurable.comp_aemeasurable",
"MeasurableSpace",
"MeasureTheory.Measure",
"Prod",
"Prod.fst",
"Prod.instMeasurableSpace",
"measurable_fst"
] |
null | false | false | theorem | Mathlib.MeasureTheory.Group.Arithmetic | AEMeasurable.fun_add | AEMeasurable | null | 72 | [
"AEMeasurable",
"Add",
"HAdd.hAdd",
"MeasurableAdd₂",
"MeasurableSpace",
"MeasureTheory.Measure",
"instHAdd"
] | 76 | [
"AEMeasurable",
"AEMeasurable.add",
"Add",
"HAdd.hAdd",
"MeasurableAdd₂",
"MeasurableSpace",
"MeasureTheory.Measure",
"id",
"instHAdd"
] |
null | false | false | theorem | Mathlib.MeasureTheory.Group.Arithmetic | AEMeasurable.fun_const_smul | AEMeasurable | null | 68 | [
"AEMeasurable",
"HSMul.hSMul",
"MeasurableConstSMul",
"MeasurableSpace",
"MeasureTheory.Measure",
"SMul",
"instHSMul"
] | 72 | [
"AEMeasurable",
"AEMeasurable.const_smul",
"HSMul.hSMul",
"MeasurableConstSMul",
"MeasurableSpace",
"MeasureTheory.Measure",
"SMul",
"id",
"instHSMul"
] |
null | false | false | theorem | Mathlib.MeasureTheory.Group.Arithmetic | AEMeasurable.fun_const_vadd | AEMeasurable | null | 68 | [
"AEMeasurable",
"HVAdd.hVAdd",
"MeasurableConstVAdd",
"MeasurableSpace",
"MeasureTheory.Measure",
"VAdd",
"instHVAdd"
] | 72 | [
"AEMeasurable",
"AEMeasurable.const_vadd",
"HVAdd.hVAdd",
"MeasurableConstVAdd",
"MeasurableSpace",
"MeasureTheory.Measure",
"VAdd",
"id",
"instHVAdd"
] |
null | false | false | theorem | Mathlib.MeasureTheory.Group.Arithmetic | AEMeasurable.fun_div | AEMeasurable | null | 72 | [
"AEMeasurable",
"Div",
"HDiv.hDiv",
"MeasurableDiv₂",
"MeasurableSpace",
"MeasureTheory.Measure",
"instHDiv"
] | 76 | [
"AEMeasurable",
"AEMeasurable.div",
"Div",
"HDiv.hDiv",
"MeasurableDiv₂",
"MeasurableSpace",
"MeasureTheory.Measure",
"id",
"instHDiv"
] |
null | false | false | theorem | Mathlib.MeasureTheory.Order.Lattice | AEMeasurable.fun_inf | AEMeasurable | null | 67 | [
"AEMeasurable",
"MeasurableInf₂",
"MeasurableSpace",
"MeasureTheory.Measure",
"Min",
"Min.min"
] | 71 | [
"AEMeasurable",
"AEMeasurable.inf",
"MeasurableInf₂",
"MeasurableSpace",
"MeasureTheory.Measure",
"Min",
"Min.min",
"id"
] |
null | false | false | theorem | Mathlib.MeasureTheory.Group.Arithmetic | AEMeasurable.fun_inv | AEMeasurable | null | 54 | [
"AEMeasurable",
"Inv",
"Inv.inv",
"MeasurableInv",
"MeasurableSpace",
"MeasureTheory.Measure"
] | 58 | [
"AEMeasurable",
"AEMeasurable.inv",
"Inv",
"Inv.inv",
"MeasurableInv",
"MeasurableSpace",
"MeasureTheory.Measure",
"id"
] |
null | false | false | theorem | Mathlib.MeasureTheory.Group.Arithmetic | AEMeasurable.fun_mul | AEMeasurable | null | 72 | [
"AEMeasurable",
"HMul.hMul",
"MeasurableMul₂",
"MeasurableSpace",
"MeasureTheory.Measure",
"Mul",
"instHMul"
] | 76 | [
"AEMeasurable",
"AEMeasurable.mul",
"HMul.hMul",
"MeasurableMul₂",
"MeasurableSpace",
"MeasureTheory.Measure",
"Mul",
"id",
"instHMul"
] |
null | false | false | theorem | Mathlib.MeasureTheory.Group.Arithmetic | AEMeasurable.fun_neg | AEMeasurable | null | 54 | [
"AEMeasurable",
"MeasurableNeg",
"MeasurableSpace",
"MeasureTheory.Measure",
"Neg",
"Neg.neg"
] | 58 | [
"AEMeasurable",
"AEMeasurable.neg",
"MeasurableNeg",
"MeasurableSpace",
"MeasureTheory.Measure",
"Neg",
"Neg.neg",
"id"
] |
null | false | false | theorem | Mathlib.MeasureTheory.Group.Arithmetic | AEMeasurable.fun_smul | AEMeasurable | null | 84 | [
"AEMeasurable",
"HSMul.hSMul",
"MeasurableSMul₂",
"MeasurableSpace",
"MeasureTheory.Measure",
"SMul",
"instHSMul"
] | 88 | [
"AEMeasurable",
"AEMeasurable.smul",
"HSMul.hSMul",
"MeasurableSMul₂",
"MeasurableSpace",
"MeasureTheory.Measure",
"SMul",
"id",
"instHSMul"
] |
null | false | false | theorem | Mathlib.MeasureTheory.Group.Arithmetic | AEMeasurable.fun_sub | AEMeasurable | null | 72 | [
"AEMeasurable",
"HSub.hSub",
"MeasurableSpace",
"MeasurableSub₂",
"MeasureTheory.Measure",
"Sub",
"instHSub"
] | 76 | [
"AEMeasurable",
"AEMeasurable.sub",
"HSub.hSub",
"MeasurableSpace",
"MeasurableSub₂",
"MeasureTheory.Measure",
"Sub",
"id",
"instHSub"
] |
null | false | false | theorem | Mathlib.MeasureTheory.Order.Lattice | AEMeasurable.fun_sup | AEMeasurable | null | 67 | [
"AEMeasurable",
"Max",
"Max.max",
"MeasurableSpace",
"MeasurableSup₂",
"MeasureTheory.Measure"
] | 71 | [
"AEMeasurable",
"AEMeasurable.sup",
"Max",
"Max.max",
"MeasurableSpace",
"MeasurableSup₂",
"MeasureTheory.Measure",
"id"
] |
null | false | false | theorem | Mathlib.MeasureTheory.Group.Arithmetic | AEMeasurable.fun_vadd | AEMeasurable | null | 84 | [
"AEMeasurable",
"HVAdd.hVAdd",
"MeasurableSpace",
"MeasurableVAdd₂",
"MeasureTheory.Measure",
"VAdd",
"instHVAdd"
] | 88 | [
"AEMeasurable",
"AEMeasurable.vadd",
"HVAdd.hVAdd",
"MeasurableSpace",
"MeasurableVAdd₂",
"MeasureTheory.Measure",
"VAdd",
"id",
"instHVAdd"
] |
null | false | false | theorem | Mathlib.MeasureTheory.Constructions.BorelSpace.Order | AEMeasurable.iInf | AEMeasurable | null | 102 | [
"AEMeasurable",
"BorelSpace",
"ConditionallyCompleteLattice.toConditionallyCompletePartialOrder",
"ConditionallyCompleteLinearOrder",
"ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice",
"ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderInf",
"ConditionallyCompleteParti... | 134 | [
"AEMeasurable",
"AEMeasurable.iSup",
"BorelSpace",
"ConditionallyCompleteLattice.toConditionallyCompletePartialOrder",
"ConditionallyCompleteLattice.toLattice",
"ConditionallyCompleteLinearOrder",
"ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice",
"ConditionallyCompletePartialOrder.toC... |
null | false | false | theorem | Mathlib.MeasureTheory.Constructions.BorelSpace.Order | AEMeasurable.iSup | AEMeasurable | null | 101 | [
"AEMeasurable",
"BorelSpace",
"ConditionallyCompleteLattice.toConditionallyCompletePartialOrder",
"ConditionallyCompleteLinearOrder",
"ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice",
"ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderSup",
"ConditionallyCompleteParti... | 538 | [
"AEMeasurable",
"AEMeasurable.ae_eq_mk",
"AEMeasurable.measurable_mk",
"AEMeasurable.mk",
"And",
"And.intro",
"BorelSpace",
"ConditionallyCompleteLattice.toConditionallyCompletePartialOrder",
"ConditionallyCompleteLinearOrder",
"ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice",
"... |
null | false | false | theorem | Mathlib.MeasureTheory.Measure.AEMeasurable | AEMeasurable.iUnion | AEMeasurable | null | 58 | [
"AEMeasurable",
"Countable",
"MeasurableSpace",
"MeasureTheory.Measure",
"MeasureTheory.Measure.restrict",
"Set",
"Set.iUnion"
] | 94 | [
"AEMeasurable",
"AEMeasurable.mono_measure",
"AEMeasurable.sum_measure",
"Countable",
"MeasurableSpace",
"MeasureTheory.Measure",
"MeasureTheory.Measure.restrict",
"MeasureTheory.Measure.restrict_iUnion_le",
"MeasureTheory.Measure.sum",
"Set",
"Set.iUnion"
] |
null | false | false | theorem | Mathlib.MeasureTheory.Function.SpecialFunctions.RCLike | AEMeasurable.im | AEMeasurable | null | 110 | [
"AEMeasurable",
"AddCommMonoid.toAddMonoid",
"AddMonoid.toAddSemigroup",
"AddMonoid.toAddZeroClass",
"AddMonoid.toZero",
"AddMonoidHom",
"AddMonoidHom.instFunLike",
"AddSemigroup.toAdd",
"AddZero.mk",
"AddZeroClass.toAddZero",
"CommRing.toRing",
"DFunLike.coe",
"DenselyNormedField.toNormedFi... | 117 | [
"AEMeasurable",
"AddCommMonoid.toAddMonoid",
"AddMonoid.toAddSemigroup",
"AddMonoid.toAddZeroClass",
"AddMonoid.toZero",
"AddMonoidHom",
"AddMonoidHom.instFunLike",
"AddSemigroup.toAdd",
"AddZero.mk",
"AddZeroClass.toAddZero",
"CommRing.toRing",
"DFunLike.coe",
"DenselyNormedField.toNormedFi... |
null | false | false | theorem | Mathlib.MeasureTheory.Measure.AEMeasurable | AEMeasurable.indicator | AEMeasurable | null | 57 | [
"AEMeasurable",
"MeasurableSet",
"MeasurableSpace",
"MeasureTheory.Measure",
"Set",
"Set.indicator",
"Zero"
] | 88 | [
"AEMeasurable",
"AEMeasurable.restrict",
"Iff.mpr",
"MeasurableSet",
"MeasurableSpace",
"MeasureTheory.Measure",
"MeasureTheory.Measure.restrict",
"Set",
"Set.indicator",
"Zero",
"aemeasurable_indicator_iff"
] |
null | false | false | theorem | Mathlib.MeasureTheory.Measure.AEMeasurable | AEMeasurable.indicator₀ | AEMeasurable | null | 58 | [
"AEMeasurable",
"MeasurableSpace",
"MeasureTheory.Measure",
"MeasureTheory.NullMeasurableSet",
"Set",
"Set.indicator",
"Zero"
] | 89 | [
"AEMeasurable",
"AEMeasurable.restrict",
"Iff.mpr",
"MeasurableSpace",
"MeasureTheory.Measure",
"MeasureTheory.Measure.restrict",
"MeasureTheory.NullMeasurableSet",
"Set",
"Set.indicator",
"Zero",
"aemeasurable_indicator_iff₀"
] |
null | false | false | theorem | Mathlib.MeasureTheory.Order.Lattice | AEMeasurable.inf | AEMeasurable | null | 71 | [
"AEMeasurable",
"MeasurableInf₂",
"MeasurableSpace",
"MeasureTheory.Measure",
"Min",
"Min.min",
"Pi.instMinForall_mathlib"
] | 112 | [
"AEMeasurable",
"AEMeasurable.prodMk",
"Measurable.comp_aemeasurable",
"MeasurableInf₂",
"MeasurableInf₂.measurable_inf",
"MeasurableSpace",
"MeasureTheory.Measure",
"Min",
"Min.min",
"Prod",
"Prod.fst",
"Prod.instMeasurableSpace",
"Prod.mk",
"Prod.snd"
] |
null | false | false | theorem | Mathlib.MeasureTheory.Order.Lattice | AEMeasurable.inf' | AEMeasurable | null | 71 | [
"AEMeasurable",
"MeasurableInf₂",
"MeasurableSpace",
"MeasureTheory.Measure",
"Min",
"Min.min",
"Pi.instMinForall_mathlib"
] | 1 | [
"AEMeasurable.inf"
] |
null | false | false | theorem | Mathlib.MeasureTheory.Order.Lattice | AEMeasurable.inf_const | AEMeasurable | null | 57 | [
"AEMeasurable",
"MeasurableInf",
"MeasurableSpace",
"MeasureTheory.Measure",
"Min",
"Min.min"
] | 68 | [
"AEMeasurable",
"Measurable.comp_aemeasurable",
"MeasurableInf",
"MeasurableInf.measurable_inf_const",
"MeasurableSpace",
"MeasureTheory.Measure",
"Min",
"Min.min"
] |
null | false | false | theorem | Mathlib.MeasureTheory.Function.SpecialFunctions.Inner | AEMeasurable.inner | AEMeasurable | null | 120 | [
"AEMeasurable",
"Inner.inner",
"InnerProductSpace",
"InnerProductSpace.toInner",
"MeasurableSpace",
"MeasureTheory.Measure",
"NormedAddCommGroup",
"NormedAddCommGroup.toSeminormedAddCommGroup",
"OpensMeasurableSpace",
"PseudoMetricSpace.toUniformSpace",
"RCLike",
"RCLike.measurableSpace",
"S... | 200 | [
"AEMeasurable",
"AEMeasurable.prodMk",
"Inner.inner",
"InnerProductSpace",
"InnerProductSpace.toInner",
"Measurable.comp_aemeasurable'",
"Measurable.fst",
"Measurable.inner",
"Measurable.snd",
"MeasurableSpace",
"MeasureTheory.Measure",
"NormedAddCommGroup",
"NormedAddCommGroup.toSeminormedA... |
null | false | false | theorem | Mathlib.MeasureTheory.Function.SpecialFunctions.Inner | AEMeasurable.inner_const | AEMeasurable | null | 109 | [
"AEMeasurable",
"Inner.inner",
"InnerProductSpace",
"InnerProductSpace.toInner",
"MeasurableSpace",
"MeasureTheory.Measure",
"NormedAddCommGroup",
"NormedAddCommGroup.toSeminormedAddCommGroup",
"OpensMeasurableSpace",
"PseudoMetricSpace.toUniformSpace",
"RCLike",
"RCLike.measurableSpace",
"S... | 108 | [
"AEMeasurable",
"AEMeasurable.inner",
"InnerProductSpace",
"MeasurableSpace",
"MeasureTheory.Measure",
"NormedAddCommGroup",
"NormedAddCommGroup.toSeminormedAddCommGroup",
"OpensMeasurableSpace",
"PseudoMetricSpace.toUniformSpace",
"RCLike",
"SecondCountableTopology",
"SeminormedAddCommGroup.t... |
null | false | false | theorem | Mathlib.MeasureTheory.Group.Arithmetic | AEMeasurable.inv | AEMeasurable | null | 59 | [
"AEMeasurable",
"Inv",
"Inv.inv",
"MeasurableInv",
"MeasurableSpace",
"MeasureTheory.Measure",
"Pi.instInv"
] | 61 | [
"AEMeasurable",
"Inv",
"Inv.inv",
"Measurable.comp_aemeasurable",
"MeasurableInv",
"MeasurableInv.measurable_inv",
"MeasurableSpace",
"MeasureTheory.Measure"
] |
null | false | false | theorem | Mathlib.MeasureTheory.Constructions.BorelSpace.Order | AEMeasurable.isGLB | AEMeasurable | null | 143 | [
"AEMeasurable",
"BorelSpace",
"Countable",
"DistribLattice.toLattice",
"Eq",
"Exists",
"Filter.Eventually",
"IsGLB",
"Lattice.toSemilatticeInf",
"LinearOrder",
"MeasurableSpace",
"MeasureTheory.Measure",
"MeasureTheory.Measure.instFunLike",
"MeasureTheory.Measure.instOuterMeasureClass",
... | 183 | [
"AEMeasurable",
"AEMeasurable.isLUB",
"BorelSpace",
"Countable",
"DistribLattice.toLattice",
"Eq",
"Exists",
"Filter.Eventually",
"IsGLB",
"Lattice.toSemilatticeInf",
"LinearOrder",
"LinearOrder.toPartialOrder",
"MeasurableSpace",
"MeasureTheory.Measure",
"MeasureTheory.Measure.instFunLi... |
null | false | false | theorem | Mathlib.MeasureTheory.Constructions.BorelSpace.Order | AEMeasurable.isLUB | AEMeasurable | null | 143 | [
"AEMeasurable",
"BorelSpace",
"Countable",
"DistribLattice.toLattice",
"Eq",
"Exists",
"Filter.Eventually",
"IsLUB",
"Lattice.toSemilatticeInf",
"LinearOrder",
"MeasurableSpace",
"MeasureTheory.Measure",
"MeasureTheory.Measure.instFunLike",
"MeasureTheory.Measure.instOuterMeasureClass",
... | 1,423 | [
"AEMeasurable",
"AEMeasurable.mk",
"And",
"And.intro",
"BorelSpace",
"Classical.propDecidable",
"Countable",
"DistribLattice.toLattice",
"EmptyCollection.emptyCollection",
"Eq",
"Eq.ge",
"Eq.mp",
"Eq.mpr",
"Eq.trans",
"Exists",
"Exists.intro",
"False",
"Filter",
"Filter.Eventuall... |
null | false | false | theorem | Mathlib.MeasureTheory.Order.Group.Lattice | AEMeasurable.leOnePart | AEMeasurable | null | 88 | [
"AEMeasurable",
"DivInvOneMonoid.toInvOneClass",
"DivisionMonoid.toDivInvOneMonoid",
"Group",
"Group.toDivInvMonoid",
"Group.toDivisionMonoid",
"InvOneClass.toInv",
"Lattice",
"Lattice.toSemilatticeSup",
"LeOnePart.leOnePart",
"MeasurableInv",
"MeasurableSpace",
"MeasurableSup",
"MeasureTh... | 133 | [
"AEMeasurable",
"AEMeasurable.inv",
"AEMeasurable.sup_const",
"DivInvOneMonoid.toInvOneClass",
"DivisionMonoid.toDivInvOneMonoid",
"Group",
"Group.toDivisionMonoid",
"Inv.inv",
"InvOneClass.toInv",
"InvOneClass.toOne",
"Lattice",
"Lattice.toSemilatticeSup",
"MeasurableInv",
"MeasurableSpac... |
null | false | false | theorem | Mathlib.MeasureTheory.Measure.Prod | AEMeasurable.lintegral_prod_left | AEMeasurable | null | 87 | [
"AEMeasurable",
"ENNReal",
"ENNReal.measurableSpace",
"Function.uncurry",
"MeasurableSpace",
"MeasureTheory.Measure",
"MeasureTheory.Measure.prod",
"MeasureTheory.SFinite",
"MeasureTheory.lintegral",
"Prod",
"Prod.instMeasurableSpace"
] | 86 | [
"AEMeasurable",
"AEMeasurable.lintegral_prod_left'",
"ENNReal",
"ENNReal.measurableSpace",
"Function.uncurry",
"MeasurableSpace",
"MeasureTheory.Measure",
"MeasureTheory.Measure.prod",
"MeasureTheory.SFinite",
"Prod",
"Prod.instMeasurableSpace"
] |
null | false | false | theorem | Mathlib.MeasureTheory.Measure.Prod | AEMeasurable.lintegral_prod_left' | AEMeasurable | null | 88 | [
"AEMeasurable",
"ENNReal",
"ENNReal.measurableSpace",
"MeasurableSpace",
"MeasureTheory.Measure",
"MeasureTheory.Measure.prod",
"MeasureTheory.SFinite",
"MeasureTheory.lintegral",
"Prod",
"Prod.instMeasurableSpace",
"Prod.mk"
] | 100 | [
"AEMeasurable",
"AEMeasurable.lintegral_prod_right'",
"AEMeasurable.prod_swap",
"ENNReal",
"ENNReal.measurableSpace",
"MeasurableSpace",
"MeasureTheory.Measure",
"MeasureTheory.Measure.prod",
"MeasureTheory.SFinite",
"Prod",
"Prod.instMeasurableSpace",
"Prod.swap"
] |
null | false | false | theorem | Mathlib.MeasureTheory.Measure.Prod | AEMeasurable.lintegral_prod_right | AEMeasurable | null | 81 | [
"AEMeasurable",
"ENNReal",
"ENNReal.measurableSpace",
"Function.uncurry",
"MeasurableSpace",
"MeasureTheory.Measure",
"MeasureTheory.Measure.prod",
"MeasureTheory.SFinite",
"MeasureTheory.lintegral",
"Prod",
"Prod.instMeasurableSpace"
] | 79 | [
"AEMeasurable",
"AEMeasurable.lintegral_prod_right'",
"ENNReal",
"ENNReal.measurableSpace",
"Function.uncurry",
"MeasurableSpace",
"MeasureTheory.Measure",
"MeasureTheory.Measure.prod",
"MeasureTheory.SFinite",
"Prod",
"Prod.instMeasurableSpace"
] |
null | false | false | theorem | Mathlib.MeasureTheory.Measure.Prod | AEMeasurable.lintegral_prod_right' | AEMeasurable | null | 83 | [
"AEMeasurable",
"ENNReal",
"ENNReal.measurableSpace",
"MeasurableSpace",
"MeasureTheory.Measure",
"MeasureTheory.Measure.prod",
"MeasureTheory.SFinite",
"MeasureTheory.lintegral",
"Prod",
"Prod.instMeasurableSpace",
"Prod.mk"
] | 417 | [
"AEMeasurable",
"And",
"And.casesOn",
"And.intro",
"ENNReal",
"ENNReal.measurableSpace",
"Eq",
"Exists.casesOn",
"Exists.intro",
"Filter.Eventually",
"Filter.Eventually.mono",
"Filter.EventuallyEq",
"Measurable",
"Measurable.lintegral_prod_right",
"MeasurableSpace",
"MeasureTheory.Meas... |
null | false | false | theorem | Mathlib.MeasureTheory.Function.SpecialFunctions.Basic | AEMeasurable.log | AEMeasurable | null | 36 | [
"AEMeasurable",
"MeasurableSpace",
"MeasureTheory.Measure",
"Real",
"Real.log",
"Real.measurableSpace"
] | 40 | [
"AEMeasurable",
"Measurable.comp_aemeasurable",
"MeasurableSpace",
"MeasureTheory.Measure",
"Real",
"Real.log",
"Real.measurableSpace",
"Real.measurable_log"
] |
null | false | false | theorem | Mathlib.MeasureTheory.Order.Group.Lattice | AEMeasurable.mabs | AEMeasurable | null | 83 | [
"AEMeasurable",
"DivInvOneMonoid.toInvOneClass",
"DivisionMonoid.toDivInvOneMonoid",
"Group",
"Group.toDivisionMonoid",
"InvOneClass.toInv",
"Lattice",
"Lattice.toSemilatticeSup",
"MeasurableInv",
"MeasurableSpace",
"MeasurableSup₂",
"MeasureTheory.Measure",
"SemilatticeSup.toMax",
"mabs"
... | 92 | [
"AEMeasurable",
"DivInvOneMonoid.toInvOneClass",
"DivisionMonoid.toDivInvOneMonoid",
"Group",
"Group.toDivisionMonoid",
"InvOneClass.toInv",
"Lattice",
"Lattice.toSemilatticeSup",
"Measurable.comp_aemeasurable",
"MeasurableInv",
"MeasurableSpace",
"MeasurableSup₂",
"MeasureTheory.Measure",
... |
null | false | false | theorem | Mathlib.MeasureTheory.Measure.AEMeasurable | AEMeasurable.map_add₀ | AEMeasurable | null | 87 | [
"AEMeasurable",
"Eq",
"HAdd.hAdd",
"MeasurableSpace",
"MeasureTheory.Measure",
"MeasureTheory.Measure.instAdd",
"MeasureTheory.Measure.map",
"instHAdd"
] | 308 | [
"AEMeasurable",
"And",
"DFunLike.coe",
"ENNReal",
"ENNReal.instAdd",
"Eq",
"Eq.trans",
"HAdd.hAdd",
"MeasurableSet",
"MeasurableSpace",
"MeasureTheory.Measure",
"MeasureTheory.Measure.ext",
"MeasureTheory.Measure.instAdd",
"MeasureTheory.Measure.instFunLike",
"MeasureTheory.Measure.map",... |
null | false | false | theorem | Mathlib.MeasureTheory.Measure.AEMeasurable | AEMeasurable.map_map_of_aemeasurable | AEMeasurable | null | 90 | [
"AEMeasurable",
"Eq",
"Function.comp",
"MeasurableSpace",
"MeasureTheory.Measure",
"MeasureTheory.Measure.map"
] | 370 | [
"AEMeasurable",
"AEMeasurable.comp_aemeasurable",
"AEMeasurable.nullMeasurable",
"DFunLike.coe",
"ENNReal",
"Eq",
"Eq.mpr",
"Eq.refl",
"Function.comp",
"MeasurableSet",
"MeasurableSpace",
"MeasureTheory.Measure",
"MeasureTheory.Measure.ext",
"MeasureTheory.Measure.instFunLike",
"MeasureT... |
null | false | false | theorem | Mathlib.MeasureTheory.Constructions.BorelSpace.Order | AEMeasurable.max | AEMeasurable | null | 107 | [
"AEMeasurable",
"DistribLattice.toLattice",
"Lattice.toSemilatticeInf",
"Lattice.toSemilatticeSup",
"LinearOrder",
"Max.max",
"MeasurableSpace",
"MeasureTheory.Measure",
"OpensMeasurableSpace",
"OrderClosedTopology",
"PartialOrder.toPreorder",
"SecondCountableTopology",
"SemilatticeInf.toPar... | 261 | [
"AEMeasurable",
"AEMeasurable.ae_eq_mk",
"AEMeasurable.measurable_mk",
"AEMeasurable.mk",
"And",
"And.intro",
"DistribLattice.toLattice",
"Exists.intro",
"Filter.EventuallyEq",
"Filter.EventuallyEq.comp₂",
"Lattice.toSemilatticeInf",
"Lattice.toSemilatticeSup",
"LinearOrder",
"Max.max",
... |
null | false | false | theorem | Mathlib.MeasureTheory.Measure.MeasureSpaceDef | AEMeasurable.measurable_mk | AEMeasurable | null | 45 | [
"AEMeasurable",
"AEMeasurable.mk",
"Measurable",
"MeasurableSpace",
"MeasureTheory.Measure"
] | 96 | [
"AEMeasurable",
"And",
"And.left",
"Classical.choose",
"Classical.choose_spec",
"Filter.EventuallyEq",
"Measurable",
"MeasurableSpace",
"MeasureTheory.Measure",
"MeasureTheory.Measure.instFunLike",
"MeasureTheory.Measure.instOuterMeasureClass",
"MeasureTheory.ae"
] |
null | false | false | theorem | Mathlib.MeasureTheory.Constructions.BorelSpace.Order | AEMeasurable.min | AEMeasurable | null | 106 | [
"AEMeasurable",
"DistribLattice.toLattice",
"Lattice.toSemilatticeInf",
"LinearOrder",
"MeasurableSpace",
"MeasureTheory.Measure",
"Min.min",
"OpensMeasurableSpace",
"OrderClosedTopology",
"PartialOrder.toPreorder",
"SecondCountableTopology",
"SemilatticeInf.toMin",
"SemilatticeInf.toPartial... | 260 | [
"AEMeasurable",
"AEMeasurable.ae_eq_mk",
"AEMeasurable.measurable_mk",
"AEMeasurable.mk",
"And",
"And.intro",
"DistribLattice.toLattice",
"Exists.intro",
"Filter.EventuallyEq",
"Filter.EventuallyEq.comp₂",
"Lattice.toSemilatticeInf",
"LinearOrder",
"Measurable",
"Measurable.min",
"Measur... |
10 | false | false | definition | Mathlib.MeasureTheory.Measure.MeasureSpaceDef | AEMeasurable.mk | AEMeasurable | regular | 32 | [
"AEMeasurable",
"MeasurableSpace",
"MeasureTheory.Measure"
] | 67 | [
"AEMeasurable",
"And",
"Classical.choose",
"Filter.EventuallyEq",
"Measurable",
"MeasurableSpace",
"MeasureTheory.Measure",
"MeasureTheory.Measure.instFunLike",
"MeasureTheory.Measure.instOuterMeasureClass",
"MeasureTheory.ae"
] |
null | true | false | theorem | Mathlib.MeasureTheory.Function.AEMeasurableSequence | AEMeasurable.mk.congr_simp | AEMeasurable.mk | null | 107 | [
"AEMeasurable",
"AEMeasurable.mk",
"Eq",
"Eq.ndrec",
"MeasurableSpace",
"MeasureTheory.Measure"
] | 222 | [
"AEMeasurable",
"AEMeasurable.mk",
"Eq",
"Eq.ndrec",
"Eq.rec",
"Eq.refl",
"MeasurableSpace",
"MeasureTheory.Measure"
] |
null | false | false | theorem | Mathlib.MeasureTheory.Measure.AEMeasurable | AEMeasurable.mono' | AEMeasurable | null | 47 | [
"AEMeasurable",
"MeasurableSpace",
"MeasureTheory.Measure",
"MeasureTheory.Measure.AbsolutelyContinuous"
] | 159 | [
"AEMeasurable",
"AEMeasurable.ae_eq_mk",
"AEMeasurable.measurable_mk",
"AEMeasurable.mk",
"And",
"And.intro",
"Compl.compl",
"Eq",
"Exists.intro",
"Filter.EventuallyEq",
"Measurable",
"MeasurableSpace",
"MeasureTheory.Measure",
"MeasureTheory.Measure.AbsolutelyContinuous",
"MeasureTheory... |
null | false | false | theorem | Mathlib.MeasureTheory.Measure.AEMeasurable | AEMeasurable.mono_ac | AEMeasurable | null | 48 | [
"AEMeasurable",
"MeasurableSpace",
"MeasureTheory.Measure",
"MeasureTheory.Measure.AbsolutelyContinuous"
] | 157 | [
"AEMeasurable",
"AEMeasurable.ae_eq_mk",
"AEMeasurable.measurable_mk",
"AEMeasurable.mk",
"And",
"And.intro",
"Eq",
"Exists.intro",
"Filter.EventuallyEq",
"Measurable",
"MeasurableSpace",
"MeasureTheory.Measure",
"MeasureTheory.Measure.AbsolutelyContinuous",
"MeasureTheory.Measure.Absolute... |
null | false | false | theorem | Mathlib.MeasureTheory.Measure.AEMeasurable | AEMeasurable.mono_measure | AEMeasurable | null | 58 | [
"AEMeasurable",
"LE.le",
"MeasurableSpace",
"MeasureTheory.Measure",
"MeasureTheory.Measure.instPartialOrder",
"PartialOrder.toPreorder",
"Preorder.toLE"
] | 69 | [
"AEMeasurable",
"AEMeasurable.mono_ac",
"LE.le",
"LE.le.absolutelyContinuous",
"MeasurableSpace",
"MeasureTheory.Measure",
"MeasureTheory.Measure.instPartialOrder",
"PartialOrder.toPreorder",
"Preorder.toLE"
] |
null | false | false | theorem | Mathlib.MeasureTheory.Measure.AEMeasurable | AEMeasurable.mono_set | AEMeasurable | null | 63 | [
"AEMeasurable",
"LE.le",
"MeasurableSpace",
"MeasureTheory.Measure",
"MeasureTheory.Measure.restrict",
"Set",
"Set.instLE"
] | 89 | [
"AEMeasurable",
"AEMeasurable.mono_measure",
"LE.le",
"MeasurableSpace",
"MeasureTheory.Measure",
"MeasureTheory.Measure.instPartialOrder",
"MeasureTheory.Measure.restrict",
"MeasureTheory.Measure.restrict_mono",
"PartialOrder.toPreorder",
"Set",
"Set.instLE",
"le_rfl"
] |
null | false | false | theorem | Mathlib.MeasureTheory.Group.Arithmetic | AEMeasurable.mul | AEMeasurable | null | 75 | [
"AEMeasurable",
"HMul.hMul",
"MeasurableMul₂",
"MeasurableSpace",
"MeasureTheory.Measure",
"Mul",
"Pi.instMul",
"instHMul"
] | 117 | [
"AEMeasurable",
"AEMeasurable.prodMk",
"HMul.hMul",
"Measurable.comp_aemeasurable",
"MeasurableMul₂",
"MeasurableMul₂.measurable_mul",
"MeasurableSpace",
"MeasureTheory.Measure",
"Mul",
"Prod",
"Prod.fst",
"Prod.instMeasurableSpace",
"Prod.mk",
"Prod.snd",
"instHMul"
] |
null | false | false | theorem | Mathlib.MeasureTheory.Group.Arithmetic | AEMeasurable.mul' | AEMeasurable | null | 75 | [
"AEMeasurable",
"HMul.hMul",
"MeasurableMul₂",
"MeasurableSpace",
"MeasureTheory.Measure",
"Mul",
"Pi.instMul",
"instHMul"
] | 1 | [
"AEMeasurable.mul"
] |
null | false | false | theorem | Mathlib.MeasureTheory.Group.Arithmetic | AEMeasurable.mul_const | AEMeasurable | null | 62 | [
"AEMeasurable",
"HMul.hMul",
"MeasurableMul",
"MeasurableSpace",
"MeasureTheory.Measure",
"Mul",
"instHMul"
] | 73 | [
"AEMeasurable",
"HMul.hMul",
"Measurable.comp_aemeasurable",
"MeasurableMul",
"MeasurableMul.measurable_mul_const",
"MeasurableSpace",
"MeasureTheory.Measure",
"Mul",
"instHMul"
] |
null | false | false | theorem | Mathlib.MeasureTheory.Group.Arithmetic | AEMeasurable.mul_iff_left | AEMeasurable | null | 122 | [
"AEMeasurable",
"CommGroup",
"CommGroup.toDivisionCommMonoid",
"CommGroup.toGroup",
"DivInvMonoid.toMonoid",
"DivInvOneMonoid.toInvOneClass",
"DivisionCommMonoid.toDivisionMonoid",
"DivisionMonoid.toDivInvOneMonoid",
"Group.toDivInvMonoid",
"HMul.hMul",
"Iff",
"InvOneClass.toInv",
"Measurabl... | 184 | [
"AEMeasurable",
"AEMeasurable.mul_iff_right",
"CommGroup",
"CommGroup.toCommMonoid",
"CommGroup.toDivisionCommMonoid",
"CommGroup.toGroup",
"CommMagma.toMul",
"CommMonoid.toCommSemigroup",
"CommSemigroup.toCommMagma",
"DivInvMonoid.toMonoid",
"DivInvOneMonoid.toInvOneClass",
"DivisionCommMonoi... |
null | false | false | theorem | Mathlib.MeasureTheory.Group.Arithmetic | AEMeasurable.mul_iff_right | AEMeasurable | null | 122 | [
"AEMeasurable",
"CommGroup",
"CommGroup.toDivisionCommMonoid",
"CommGroup.toGroup",
"DivInvMonoid.toMonoid",
"DivInvOneMonoid.toInvOneClass",
"DivisionCommMonoid.toDivisionMonoid",
"DivisionMonoid.toDivInvOneMonoid",
"Group.toDivInvMonoid",
"HMul.hMul",
"Iff",
"InvOneClass.toInv",
"Measurabl... | 321 | [
"AEMeasurable",
"AEMeasurable.inv",
"AEMeasurable.mul",
"CommGroup",
"CommGroup.toDivisionCommMonoid",
"CommGroup.toGroup",
"DivInvMonoid.toMonoid",
"DivInvOneMonoid.toInvOneClass",
"DivisionCommMonoid.toDivisionMonoid",
"DivisionMonoid.toDivInvOneMonoid",
"Eq",
"Eq.rec",
"Eq.symm",
"Eq.tr... |
null | false | false | theorem | Mathlib.MeasureTheory.Group.Arithmetic | AEMeasurable.neg | AEMeasurable | null | 59 | [
"AEMeasurable",
"MeasurableNeg",
"MeasurableSpace",
"MeasureTheory.Measure",
"Neg",
"Neg.neg",
"Pi.instNeg"
] | 61 | [
"AEMeasurable",
"Measurable.comp_aemeasurable",
"MeasurableNeg",
"MeasurableNeg.measurable_neg",
"MeasurableSpace",
"MeasureTheory.Measure",
"Neg",
"Neg.neg"
] |
null | false | false | theorem | Mathlib.MeasureTheory.Order.Group.Lattice | AEMeasurable.negPart | AEMeasurable | null | 88 | [
"AEMeasurable",
"AddGroup",
"AddGroup.toSubNegMonoid",
"AddGroup.toSubtractionMonoid",
"Lattice",
"Lattice.toSemilatticeSup",
"MeasurableNeg",
"MeasurableSpace",
"MeasurableSup",
"MeasureTheory.Measure",
"NegPart.negPart",
"NegZeroClass.toNeg",
"SemilatticeSup.toMax",
"SubNegZeroMonoid.toN... | 133 | [
"AEMeasurable",
"AEMeasurable.neg",
"AEMeasurable.sup_const",
"AddGroup",
"AddGroup.toSubtractionMonoid",
"Lattice",
"Lattice.toSemilatticeSup",
"MeasurableNeg",
"MeasurableSpace",
"MeasurableSup",
"MeasureTheory.Measure",
"Neg.neg",
"NegZeroClass.toNeg",
"NegZeroClass.toZero",
"OfNat.of... |
null | false | false | theorem | Mathlib.MeasureTheory.Constructions.BorelSpace.Metric | AEMeasurable.nnnorm | AEMeasurable | null | 76 | [
"AEMeasurable",
"MeasurableSpace",
"MeasureTheory.Measure",
"NNNorm.nnnorm",
"NNReal",
"NNReal.measurableSpace",
"NormedAddCommGroup",
"NormedAddCommGroup.toSeminormedAddCommGroup",
"OpensMeasurableSpace",
"PseudoMetricSpace.toUniformSpace",
"SeminormedAddCommGroup.toPseudoMetricSpace",
"Semin... | 83 | [
"AEMeasurable",
"Measurable.comp_aemeasurable",
"MeasurableSpace",
"MeasureTheory.Measure",
"NNNorm.nnnorm",
"NNReal",
"NNReal.measurableSpace",
"NormedAddCommGroup",
"NormedAddCommGroup.toSeminormedAddCommGroup",
"OpensMeasurableSpace",
"PseudoMetricSpace.toUniformSpace",
"SeminormedAddCommGr... |
null | false | false | theorem | Mathlib.MeasureTheory.Constructions.BorelSpace.Real | AEMeasurable.nnreal_tsum | AEMeasurable | null | 56 | [
"AEMeasurable",
"Countable",
"MeasurableSpace",
"MeasureTheory.Measure",
"NNReal",
"NNReal.instSemiring",
"NNReal.instTopologicalSpace",
"NNReal.measurableSpace",
"Semiring.toAddCommMonoid",
"SummationFilter.unconditional",
"tsum"
] | 149 | [
"AEMeasurable",
"AEMeasurable._auto_1",
"AEMeasurable.coe_nnreal_ennreal",
"AEMeasurable.ennreal_toNNReal",
"AEMeasurable.ennreal_tsum",
"Countable",
"ENNReal",
"ENNReal.instAddCommMonoid",
"ENNReal.instTopologicalSpace",
"ENNReal.ofNNReal",
"ENNReal.toNNReal",
"Eq",
"Eq.mpr",
"MeasurableS... |
null | false | false | theorem | Mathlib.MeasureTheory.Constructions.BorelSpace.Metric | AEMeasurable.norm | AEMeasurable | null | 71 | [
"AEMeasurable",
"MeasurableSpace",
"MeasureTheory.Measure",
"Norm.norm",
"NormedAddCommGroup",
"NormedAddCommGroup.toNorm",
"NormedAddCommGroup.toSeminormedAddCommGroup",
"OpensMeasurableSpace",
"PseudoMetricSpace.toUniformSpace",
"Real",
"Real.measurableSpace",
"SeminormedAddCommGroup.toPseud... | 78 | [
"AEMeasurable",
"Measurable.comp_aemeasurable",
"MeasurableSpace",
"MeasureTheory.Measure",
"Norm.norm",
"NormedAddCommGroup",
"NormedAddCommGroup.toNorm",
"NormedAddCommGroup.toSeminormedAddCommGroup",
"OpensMeasurableSpace",
"PseudoMetricSpace.toUniformSpace",
"Real",
"Real.measurableSpace",... |
null | false | false | theorem | Mathlib.MeasureTheory.Measure.MeasureSpace | AEMeasurable.nullMeasurable | AEMeasurable | null | 38 | [
"AEMeasurable",
"MeasurableSpace",
"MeasureTheory.Measure",
"MeasureTheory.NullMeasurable"
] | 124 | [
"AEMeasurable",
"Filter.EventuallyEq",
"Filter.EventuallyEq.symm",
"Measurable",
"Measurable.nullMeasurable",
"MeasurableSpace",
"MeasureTheory.Measure",
"MeasureTheory.Measure.instFunLike",
"MeasureTheory.Measure.instOuterMeasureClass",
"MeasureTheory.NullMeasurable",
"MeasureTheory.NullMeasura... |
null | false | false | theorem | Mathlib.MeasureTheory.Measure.MeasureSpace | AEMeasurable.nullMeasurableSet_preimage | AEMeasurable | null | 50 | [
"AEMeasurable",
"MeasurableSet",
"MeasurableSpace",
"MeasureTheory.Measure",
"MeasureTheory.NullMeasurableSet",
"Set",
"Set.preimage"
] | 51 | [
"AEMeasurable",
"AEMeasurable.nullMeasurable",
"MeasurableSet",
"MeasurableSpace",
"MeasureTheory.Measure",
"Set"
] |
null | false | false | theorem | Mathlib.MeasureTheory.Measure.MeasureSpaceDef | AEMeasurable.of_discrete | AEMeasurable | null | 33 | [
"AEMeasurable",
"DiscreteMeasurableSpace",
"MeasurableSpace",
"MeasureTheory.Measure"
] | 42 | [
"DiscreteMeasurableSpace",
"Measurable.aemeasurable",
"Measurable.of_discrete",
"MeasurableSpace",
"MeasureTheory.Measure"
] |
null | false | false | theorem | Mathlib.MeasureTheory.Measure.Map | AEMeasurable.of_map_ne_zero | AEMeasurable | null | 56 | [
"AEMeasurable",
"MeasurableSpace",
"MeasureTheory.Measure",
"MeasureTheory.Measure.instZero",
"MeasureTheory.Measure.map",
"Ne",
"OfNat.ofNat",
"Zero.toOfNat0"
] | 121 | [
"AEMeasurable",
"Eq",
"Iff.mp",
"MeasurableSpace",
"MeasureTheory.Measure",
"MeasureTheory.Measure.instZero",
"MeasureTheory.Measure.map",
"MeasureTheory.Measure.map_of_not_aemeasurable",
"Ne",
"Not",
"OfNat.ofNat",
"Zero.toOfNat0",
"not_imp_comm"
] |
null | false | false | theorem | Mathlib.MeasureTheory.Order.Group.Lattice | AEMeasurable.oneLePart | AEMeasurable | null | 71 | [
"AEMeasurable",
"Group",
"Group.toDivInvMonoid",
"Lattice",
"Lattice.toSemilatticeSup",
"MeasurableSpace",
"MeasurableSup",
"MeasureTheory.Measure",
"OneLePart.oneLePart",
"SemilatticeSup.toMax",
"instOneLePart"
] | 86 | [
"AEMeasurable",
"AEMeasurable.sup_const",
"DivInvOneMonoid.toInvOneClass",
"DivisionMonoid.toDivInvOneMonoid",
"Group",
"Group.toDivisionMonoid",
"InvOneClass.toOne",
"Lattice",
"Lattice.toSemilatticeSup",
"MeasurableSpace",
"MeasurableSup",
"MeasureTheory.Measure",
"OfNat.ofNat",
"One.toO... |
null | false | false | theorem | Mathlib.MeasureTheory.Order.Group.Lattice | AEMeasurable.posPart | AEMeasurable | null | 71 | [
"AEMeasurable",
"AddGroup",
"AddGroup.toSubNegMonoid",
"Lattice",
"Lattice.toSemilatticeSup",
"MeasurableSpace",
"MeasurableSup",
"MeasureTheory.Measure",
"PosPart.posPart",
"SemilatticeSup.toMax",
"instPosPart"
] | 86 | [
"AEMeasurable",
"AEMeasurable.sup_const",
"AddGroup",
"AddGroup.toSubtractionMonoid",
"Lattice",
"Lattice.toSemilatticeSup",
"MeasurableSpace",
"MeasurableSup",
"MeasureTheory.Measure",
"NegZeroClass.toZero",
"OfNat.ofNat",
"SemilatticeSup.toMax",
"SubNegZeroMonoid.toNegZeroClass",
"Subtra... |
null | false | false | theorem | Mathlib.MeasureTheory.Group.Arithmetic | AEMeasurable.pow | AEMeasurable | null | 83 | [
"AEMeasurable",
"HPow.hPow",
"MeasurablePow",
"MeasurableSpace",
"MeasureTheory.Measure",
"Pow",
"instHPow"
] | 131 | [
"AEMeasurable",
"AEMeasurable.prodMk",
"HPow.hPow",
"Measurable.comp_aemeasurable",
"MeasurablePow",
"MeasurablePow.measurable_pow",
"MeasurableSpace",
"MeasureTheory.Measure",
"Pow",
"Prod",
"Prod.fst",
"Prod.instMeasurableSpace",
"Prod.mk",
"Prod.snd",
"instHPow"
] |
null | false | false | theorem | Mathlib.MeasureTheory.Group.Arithmetic | AEMeasurable.pow_const | AEMeasurable | null | 72 | [
"AEMeasurable",
"HPow.hPow",
"MeasurablePow",
"MeasurableSpace",
"MeasureTheory.Measure",
"Pow",
"instHPow"
] | 75 | [
"AEMeasurable",
"AEMeasurable.pow",
"MeasurablePow",
"MeasurableSpace",
"MeasureTheory.Measure",
"Pow",
"aemeasurable_const"
] |
null | false | false | theorem | Mathlib.MeasureTheory.Measure.AEMeasurable | AEMeasurable.prodMk | AEMeasurable | null | 73 | [
"AEMeasurable",
"MeasurableSpace",
"MeasureTheory.Measure",
"Prod",
"Prod.instMeasurableSpace",
"Prod.mk"
] | 230 | [
"AEMeasurable",
"AEMeasurable.ae_eq_mk",
"AEMeasurable.measurable_mk",
"AEMeasurable.mk",
"And",
"And.intro",
"Exists.intro",
"Filter.EventuallyEq",
"Filter.EventuallyEq.prodMk",
"Measurable",
"Measurable.prodMk",
"MeasurableSpace",
"MeasureTheory.Measure",
"MeasureTheory.Measure.instFunLi... |
null | false | false | theorem | Mathlib.MeasureTheory.Measure.Prod | AEMeasurable.prod_swap | AEMeasurable | null | 100 | [
"AEMeasurable",
"MeasurableSpace",
"MeasureTheory.Measure",
"MeasureTheory.Measure.prod",
"MeasureTheory.SFinite",
"Prod",
"Prod.instMeasurableSpace",
"Prod.swap"
] | 177 | [
"AEMeasurable",
"AEMeasurable.comp_measurable",
"Eq.mp",
"Eq.symm",
"MeasurableSpace",
"MeasureTheory.Measure",
"MeasureTheory.Measure.map",
"MeasureTheory.Measure.prod",
"MeasureTheory.Measure.prod_swap",
"MeasureTheory.SFinite",
"Prod",
"Prod.instMeasurableSpace",
"Prod.swap",
"congrArg"... |
null | false | false | theorem | Mathlib.MeasureTheory.Function.SpecialFunctions.RCLike | AEMeasurable.re | AEMeasurable | null | 110 | [
"AEMeasurable",
"AddCommMonoid.toAddMonoid",
"AddMonoid.toAddSemigroup",
"AddMonoid.toAddZeroClass",
"AddMonoid.toZero",
"AddMonoidHom",
"AddMonoidHom.instFunLike",
"AddSemigroup.toAdd",
"AddZero.mk",
"AddZeroClass.toAddZero",
"CommRing.toRing",
"DFunLike.coe",
"DenselyNormedField.toNormedFi... | 117 | [
"AEMeasurable",
"AddCommMonoid.toAddMonoid",
"AddMonoid.toAddSemigroup",
"AddMonoid.toAddZeroClass",
"AddMonoid.toZero",
"AddMonoidHom",
"AddMonoidHom.instFunLike",
"AddSemigroup.toAdd",
"AddZero.mk",
"AddZeroClass.toAddZero",
"CommRing.toRing",
"DFunLike.coe",
"DenselyNormedField.toNormedFi... |
null | false | false | theorem | Mathlib.MeasureTheory.Constructions.BorelSpace.Real | AEMeasurable.real_toNNReal | AEMeasurable | null | 38 | [
"AEMeasurable",
"MeasurableSpace",
"MeasureTheory.Measure",
"NNReal",
"NNReal.measurableSpace",
"Real",
"Real.measurableSpace",
"Real.toNNReal"
] | 42 | [
"AEMeasurable",
"Measurable.comp_aemeasurable",
"MeasurableSpace",
"MeasureTheory.Measure",
"NNReal",
"NNReal.measurableSpace",
"Real",
"Real.measurableSpace",
"Real.toNNReal",
"measurable_real_toNNReal"
] |
null | false | false | theorem | Mathlib.MeasureTheory.Measure.AEMeasurable | AEMeasurable.restrict | AEMeasurable | null | 46 | [
"AEMeasurable",
"MeasurableSpace",
"MeasureTheory.Measure",
"MeasureTheory.Measure.restrict",
"Set"
] | 152 | [
"AEMeasurable",
"AEMeasurable.ae_eq_mk",
"AEMeasurable.measurable_mk",
"AEMeasurable.mk",
"And",
"And.intro",
"Eq",
"Exists.intro",
"Filter.EventuallyEq",
"Measurable",
"MeasurableSpace",
"MeasureTheory.Measure",
"MeasureTheory.Measure.instFunLike",
"MeasureTheory.Measure.instOuterMeasureC... |
null | false | false | theorem | Mathlib.MeasureTheory.Function.SpecialFunctions.Basic | AEMeasurable.sin | AEMeasurable | null | 36 | [
"AEMeasurable",
"MeasurableSpace",
"MeasureTheory.Measure",
"Real",
"Real.measurableSpace",
"Real.sin"
] | 40 | [
"AEMeasurable",
"Measurable.comp_aemeasurable",
"MeasurableSpace",
"MeasureTheory.Measure",
"Real",
"Real.measurableSpace",
"Real.measurable_sin",
"Real.sin"
] |
null | false | false | theorem | Mathlib.MeasureTheory.Function.SpecialFunctions.Sinc | AEMeasurable.sinc | AEMeasurable | null | 36 | [
"AEMeasurable",
"MeasurableSpace",
"MeasureTheory.Measure",
"Real",
"Real.measurableSpace",
"Real.sinc"
] | 40 | [
"AEMeasurable",
"Measurable.comp_aemeasurable",
"MeasurableSpace",
"MeasureTheory.Measure",
"Real",
"Real.measurableSpace",
"Real.measurable_sinc",
"Real.sinc"
] |
null | false | false | theorem | Mathlib.MeasureTheory.Measure.Decomposition.Lebesgue | AEMeasurable.singularPart | AEMeasurable | null | 46 | [
"AEMeasurable",
"MeasurableSpace",
"MeasureTheory.Measure",
"MeasureTheory.Measure.singularPart"
] | 55 | [
"AEMeasurable",
"AEMeasurable.mono_measure",
"MeasurableSpace",
"MeasureTheory.Measure",
"MeasureTheory.Measure.singularPart",
"MeasureTheory.Measure.singularPart_le"
] |
null | false | false | theorem | Mathlib.MeasureTheory.Function.SpecialFunctions.Basic | AEMeasurable.sinh | AEMeasurable | null | 36 | [
"AEMeasurable",
"MeasurableSpace",
"MeasureTheory.Measure",
"Real",
"Real.measurableSpace",
"Real.sinh"
] | 40 | [
"AEMeasurable",
"Measurable.comp_aemeasurable",
"MeasurableSpace",
"MeasureTheory.Measure",
"Real",
"Real.measurableSpace",
"Real.measurable_sinh",
"Real.sinh"
] |
null | false | false | theorem | Mathlib.MeasureTheory.Group.Arithmetic | AEMeasurable.smul | AEMeasurable | null | 91 | [
"AEMeasurable",
"HSMul.hSMul",
"MeasurableSMul₂",
"MeasurableSpace",
"MeasureTheory.Measure",
"Pi.smul'",
"SMul",
"instHSMul"
] | 130 | [
"AEMeasurable",
"AEMeasurable.prodMk",
"Function.uncurry",
"HSMul.hSMul",
"Measurable.comp_aemeasurable",
"MeasurableSMul₂",
"MeasurableSMul₂.measurable_smul",
"MeasurableSpace",
"MeasureTheory.Measure",
"Prod",
"Prod.instMeasurableSpace",
"Prod.mk",
"SMul",
"instHSMul"
] |
null | false | false | theorem | Mathlib.MeasureTheory.Group.Arithmetic | AEMeasurable.smul_const | AEMeasurable | null | 74 | [
"AEMeasurable",
"HSMul.hSMul",
"MeasurableSMul",
"MeasurableSpace",
"MeasureTheory.Measure",
"SMul",
"instHSMul"
] | 96 | [
"AEMeasurable",
"HSMul.hSMul",
"Measurable.comp_aemeasurable'",
"Measurable.smul_const",
"MeasurableSMul",
"MeasurableSpace",
"MeasureTheory.Measure",
"SMul",
"instHSMul",
"measurable_id'"
] |
null | false | false | theorem | Mathlib.MeasureTheory.Measure.AEMeasurable | AEMeasurable.smul_measure | AEMeasurable | null | 88 | [
"AEMeasurable",
"CommSemiring.toSemiring",
"Distrib.toMul",
"ENNReal",
"ENNReal.instCommSemiring",
"HSMul.hSMul",
"IsScalarTower",
"MeasurableSpace",
"MeasureTheory.Measure",
"MeasureTheory.Measure.instSMul",
"SMul",
"instDistribOfSemiring",
"instHSMul",
"instSMulOfMul"
] | 206 | [
"AEMeasurable",
"AEMeasurable.ae_eq_mk",
"AEMeasurable.measurable_mk",
"AEMeasurable.mk",
"And",
"And.intro",
"CommSemiring.toSemiring",
"Distrib.toMul",
"ENNReal",
"ENNReal.instCommSemiring",
"Eq",
"Exists.intro",
"Filter.EventuallyEq",
"HSMul.hSMul",
"IsScalarTower",
"Measurable",
... |
null | false | false | theorem | Mathlib.MeasureTheory.Measure.AEMeasurable | AEMeasurable.snd | AEMeasurable | null | 59 | [
"AEMeasurable",
"MeasurableSpace",
"MeasureTheory.Measure",
"Prod",
"Prod.instMeasurableSpace",
"Prod.snd"
] | 72 | [
"AEMeasurable",
"Measurable.comp_aemeasurable",
"MeasurableSpace",
"MeasureTheory.Measure",
"Prod",
"Prod.instMeasurableSpace",
"Prod.snd",
"measurable_snd"
] |
null | false | false | theorem | Mathlib.MeasureTheory.Function.SpecialFunctions.Basic | AEMeasurable.sqrt | AEMeasurable | null | 36 | [
"AEMeasurable",
"MeasurableSpace",
"MeasureTheory.Measure",
"Real",
"Real.measurableSpace",
"Real.sqrt"
] | 66 | [
"AEMeasurable",
"BorelSpace.opensMeasurable",
"Continuous.measurable",
"Measurable.comp_aemeasurable",
"MeasurableSpace",
"MeasureTheory.Measure",
"PseudoMetricSpace.toUniformSpace",
"Real",
"Real.borelSpace",
"Real.continuous_sqrt",
"Real.measurableSpace",
"Real.pseudoMetricSpace",
"Real.sq... |
null | false | false | theorem | Mathlib.MeasureTheory.Group.Arithmetic | AEMeasurable.sub | AEMeasurable | null | 75 | [
"AEMeasurable",
"HSub.hSub",
"MeasurableSpace",
"MeasurableSub₂",
"MeasureTheory.Measure",
"Pi.instSub",
"Sub",
"instHSub"
] | 117 | [
"AEMeasurable",
"AEMeasurable.prodMk",
"HSub.hSub",
"Measurable.comp_aemeasurable",
"MeasurableSpace",
"MeasurableSub₂",
"MeasurableSub₂.measurable_sub",
"MeasureTheory.Measure",
"Prod",
"Prod.fst",
"Prod.instMeasurableSpace",
"Prod.mk",
"Prod.snd",
"Sub",
"instHSub"
] |
null | false | false | theorem | Mathlib.MeasureTheory.Group.Arithmetic | AEMeasurable.sub' | AEMeasurable | null | 75 | [
"AEMeasurable",
"HSub.hSub",
"MeasurableSpace",
"MeasurableSub₂",
"MeasureTheory.Measure",
"Pi.instSub",
"Sub",
"instHSub"
] | 1 | [
"AEMeasurable.sub"
] |
null | false | false | theorem | Mathlib.MeasureTheory.Group.Arithmetic | AEMeasurable.sub_const | AEMeasurable | null | 62 | [
"AEMeasurable",
"HSub.hSub",
"MeasurableSpace",
"MeasurableSub",
"MeasureTheory.Measure",
"Sub",
"instHSub"
] | 73 | [
"AEMeasurable",
"HSub.hSub",
"Measurable.comp_aemeasurable",
"MeasurableSpace",
"MeasurableSub",
"MeasurableSub.measurable_sub_const",
"MeasureTheory.Measure",
"Sub",
"instHSub"
] |
null | false | false | theorem | Mathlib.MeasureTheory.Measure.AEMeasurable | AEMeasurable.subtype_mk | AEMeasurable | null | 75 | [
"AEMeasurable",
"MeasurableSpace",
"MeasureTheory.Measure",
"Membership.mem",
"Set",
"Set.Elem",
"Set.codRestrict",
"Set.instMembership",
"Subtype.instMeasurableSpace"
] | 733 | [
"AEMeasurable",
"AEMeasurable.exists_ae_eq_range_subset",
"And",
"And.casesOn",
"And.intro",
"Eq",
"Eq.mpr",
"Exists",
"Exists.casesOn",
"Exists.intro",
"Filter.Eventually.of_forall",
"Filter.EventuallyEq",
"Filter.mp_mem",
"Filter.univ_mem'",
"Inhabited.default",
"LE.le",
"Lean.Elab... |
null | false | false | theorem | Mathlib.MeasureTheory.Measure.AEMeasurable | AEMeasurable.sum_measure | AEMeasurable | null | 46 | [
"AEMeasurable",
"Countable",
"MeasurableSpace",
"MeasureTheory.Measure",
"MeasureTheory.Measure.sum"
] | 1,577 | [
"AEMeasurable",
"AEMeasurable.ae_eq_mk",
"AEMeasurable.measurable_mk",
"AEMeasurable.mk",
"And",
"And.casesOn",
"And.intro",
"Classical.propDecidable",
"Compl.compl",
"Countable",
"DFunLike.coe",
"ENNReal",
"ENNReal.instZero",
"Eq",
"Eq.mp",
"Eq.mpr",
"Eq.symm",
"Eq.trans",
"Exis... |
null | false | false | theorem | Mathlib.MeasureTheory.Order.Lattice | AEMeasurable.sup | AEMeasurable | null | 71 | [
"AEMeasurable",
"Max",
"Max.max",
"MeasurableSpace",
"MeasurableSup₂",
"MeasureTheory.Measure",
"Pi.instMaxForall_mathlib"
] | 112 | [
"AEMeasurable",
"AEMeasurable.prodMk",
"Max",
"Max.max",
"Measurable.comp_aemeasurable",
"MeasurableSpace",
"MeasurableSup₂",
"MeasurableSup₂.measurable_sup",
"MeasureTheory.Measure",
"Prod",
"Prod.fst",
"Prod.instMeasurableSpace",
"Prod.mk",
"Prod.snd"
] |
null | false | false | theorem | Mathlib.MeasureTheory.Order.Lattice | AEMeasurable.sup' | AEMeasurable | null | 71 | [
"AEMeasurable",
"Max",
"Max.max",
"MeasurableSpace",
"MeasurableSup₂",
"MeasureTheory.Measure",
"Pi.instMaxForall_mathlib"
] | 1 | [
"AEMeasurable.sup"
] |
null | false | false | theorem | Mathlib.MeasureTheory.Order.Lattice | AEMeasurable.sup_const | AEMeasurable | null | 57 | [
"AEMeasurable",
"Max",
"Max.max",
"MeasurableSpace",
"MeasurableSup",
"MeasureTheory.Measure"
] | 68 | [
"AEMeasurable",
"Max",
"Max.max",
"Measurable.comp_aemeasurable",
"MeasurableSpace",
"MeasurableSup",
"MeasurableSup.measurable_sup_const",
"MeasureTheory.Measure"
] |
null | false | false | theorem | Mathlib.MeasureTheory.Constructions.Polish.Basic | AEMeasurable.tprod | AEMeasurable | null | 113 | [
"AEMeasurable",
"BorelSpace",
"CommMonoid",
"CommMonoid.toMonoid",
"Countable",
"Filter.IsCountablyGenerated",
"Finset",
"MeasurableMul₂",
"MeasurableSpace",
"MeasureTheory.Measure",
"Monoid.toMulOneClass",
"MulOne.toMul",
"MulOneClass.toMulOne",
"SecondCountableTopology",
"SummationFilt... | 459 | [
"AEMeasurable",
"And",
"And.intro",
"And.left",
"And.right",
"BorelSpace",
"Classical.choose",
"Classical.choose_spec",
"CommMonoid",
"CommMonoid.toMonoid",
"Countable",
"Eq",
"Exists.intro",
"Filter.Eventually",
"Filter.EventuallyEq",
"Filter.IsCountablyGenerated",
"Filter.mp_mem",
... |
null | false | false | theorem | Mathlib.MeasureTheory.Constructions.Polish.Basic | AEMeasurable.tprod' | AEMeasurable | null | 115 | [
"AEMeasurable",
"BorelSpace",
"CommMonoid",
"CommMonoid.toMonoid",
"Filter.IsCountablyGenerated",
"Finset",
"MeasurableMul₂",
"MeasurableSpace",
"MeasureTheory.Measure",
"Monoid.toMulOneClass",
"MulOne.toMul",
"MulOneClass.toMulOne",
"Pi.commMonoid",
"Pi.topologicalSpace",
"SummationFilt... | 1,375 | [
"AEMeasurable",
"AEMeasurable._auto_1",
"And",
"BorelSpace",
"Classical.decPred",
"Classical.propDecidable",
"CommMonoid",
"CommMonoid.toMonoid",
"Eq",
"Eq.mpr",
"Exists.choose",
"Exists.choose_spec",
"Filter.Eventually.of_forall",
"Filter.IsCountablyGenerated",
"Filter.Tendsto",
"Filt... |
null | false | false | theorem | Mathlib.MeasureTheory.Constructions.Polish.Basic | AEMeasurable.tsum | AEMeasurable | null | 113 | [
"AEMeasurable",
"AddCommMonoid",
"AddCommMonoid.toAddMonoid",
"AddMonoid.toAddZeroClass",
"AddZero.toAdd",
"AddZeroClass.toAddZero",
"BorelSpace",
"Countable",
"Filter.IsCountablyGenerated",
"Finset",
"MeasurableAdd₂",
"MeasurableSpace",
"MeasureTheory.Measure",
"SecondCountableTopology",
... | 459 | [
"AEMeasurable",
"AddCommMonoid",
"AddCommMonoid.toAddMonoid",
"AddMonoid.toAddZeroClass",
"AddZero.toAdd",
"AddZeroClass.toAddZero",
"And",
"And.intro",
"And.left",
"And.right",
"BorelSpace",
"Classical.choose",
"Classical.choose_spec",
"Countable",
"Eq",
"Exists.intro",
"Filter.Even... |
null | false | false | theorem | Mathlib.MeasureTheory.Constructions.Polish.Basic | AEMeasurable.tsum' | AEMeasurable | null | 115 | [
"AEMeasurable",
"AddCommMonoid",
"AddCommMonoid.toAddMonoid",
"AddMonoid.toAddZeroClass",
"AddZero.toAdd",
"AddZeroClass.toAddZero",
"BorelSpace",
"Filter.IsCountablyGenerated",
"Finset",
"MeasurableAdd₂",
"MeasurableSpace",
"MeasureTheory.Measure",
"Pi.addCommMonoid",
"Pi.topologicalSpace... | 1,375 | [
"AEMeasurable",
"AEMeasurable._auto_1",
"AddCommMonoid",
"AddCommMonoid.toAddMonoid",
"AddMonoid.toAddZeroClass",
"AddZero.toAdd",
"AddZero.toZero",
"AddZeroClass.toAddZero",
"And",
"BorelSpace",
"Classical.decPred",
"Classical.propDecidable",
"Eq",
"Eq.mpr",
"Exists.choose",
"Exists.c... |
null | false | false | theorem | Mathlib.MeasureTheory.Group.Arithmetic | AEMeasurable.vadd | AEMeasurable | null | 91 | [
"AEMeasurable",
"HVAdd.hVAdd",
"MeasurableSpace",
"MeasurableVAdd₂",
"MeasureTheory.Measure",
"Pi.vadd'",
"VAdd",
"instHVAdd"
] | 130 | [
"AEMeasurable",
"AEMeasurable.prodMk",
"Function.uncurry",
"HVAdd.hVAdd",
"Measurable.comp_aemeasurable",
"MeasurableSpace",
"MeasurableVAdd₂",
"MeasurableVAdd₂.measurable_vadd",
"MeasureTheory.Measure",
"Prod",
"Prod.instMeasurableSpace",
"Prod.mk",
"VAdd",
"instHVAdd"
] |
null | false | false | theorem | Mathlib.MeasureTheory.Group.Arithmetic | AEMeasurable.vadd_const | AEMeasurable | null | 74 | [
"AEMeasurable",
"HVAdd.hVAdd",
"MeasurableSpace",
"MeasurableVAdd",
"MeasureTheory.Measure",
"VAdd",
"instHVAdd"
] | 96 | [
"AEMeasurable",
"HVAdd.hVAdd",
"Measurable.comp_aemeasurable'",
"Measurable.vadd_const",
"MeasurableSpace",
"MeasurableVAdd",
"MeasureTheory.Measure",
"VAdd",
"instHVAdd",
"measurable_id'"
] |
null | false | false | theorem | Mathlib.MeasureTheory.Measure.Decomposition.Lebesgue | AEMeasurable.withDensity_rnDeriv | AEMeasurable | null | 51 | [
"AEMeasurable",
"MeasurableSpace",
"MeasureTheory.Measure",
"MeasureTheory.Measure.rnDeriv",
"MeasureTheory.Measure.withDensity"
] | 60 | [
"AEMeasurable",
"AEMeasurable.mono_measure",
"MeasurableSpace",
"MeasureTheory.Measure",
"MeasureTheory.Measure.rnDeriv",
"MeasureTheory.Measure.withDensity",
"MeasureTheory.Measure.withDensity_rnDeriv_le"
] |
null | false | false | theorem | Mathlib.MeasureTheory.Integral.IntegrableOn | AEStronglyMeasurable.stronglyMeasurableAtFilter_of_mem | AEStronglyMeasurable | null | 65 | [
"Filter",
"Filter.instMembership",
"MeasurableSpace",
"MeasureTheory.AEStronglyMeasurable",
"MeasureTheory.Measure",
"MeasureTheory.Measure.restrict",
"Membership.mem",
"Set",
"StronglyMeasurableAtFilter",
"TopologicalSpace"
] | 110 | [
"And",
"And.intro",
"Exists.intro",
"Filter",
"Filter.instMembership",
"MeasurableSpace",
"MeasureTheory.AEStronglyMeasurable",
"MeasureTheory.Measure",
"MeasureTheory.Measure.restrict",
"Membership.mem",
"Set",
"TopologicalSpace"
] |
null | false | false | inductive | Mathlib.Data.List.AList | AList | null | 7 | [] | null | [] | |
4 | false | false | definition | Mathlib.Data.List.AList | AList.Disjoint | AList | regular | 16 | [
"AList"
] | 46 | [
"AList",
"AList.keys",
"List",
"List.instMembership",
"Membership.mem",
"Not"
] |
null | true | true | abbrev | Mathlib.Data.List.AList | AList._sizeOf_1 | AList | abbrev | 22 | [
"AList",
"Nat",
"SizeOf"
] | 89 | [
"AList",
"AList.rec",
"HAdd.hAdd",
"List",
"List.NodupKeys",
"List._sizeOf_inst",
"Nat",
"OfNat.ofNat",
"Sigma",
"Sigma._sizeOf_inst",
"SizeOf",
"SizeOf.sizeOf",
"instAddNat",
"instHAdd",
"instOfNatNat",
"instSizeOfDefault"
] |
null | true | true | abbrev | Mathlib.Data.List.AList | AList._sizeOf_inst | AList | abbrev | 22 | [
"AList",
"SizeOf"
] | 31 | [
"AList",
"AList._sizeOf_1",
"SizeOf",
"SizeOf.mk"
] |
null | true | false | abbrev | Mathlib.Data.List.AList | AList.casesOn | AList | abbrev | 39 | [
"AList",
"AList.mk",
"List",
"List.NodupKeys",
"Sigma"
] | 54 | [
"AList",
"AList.mk",
"AList.rec",
"List",
"List.NodupKeys",
"Sigma"
] |
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