Documentation Verification Report

NullMeasurable

πŸ“ Source: Mathlib/MeasureTheory/Measure/NullMeasurable.lean

Statistics

MetricCount
DefinitionsIsComplete, completion, NullMeasurable, NullMeasurableSet, NullMeasurableSpace, instInhabited, instMeasurableSpace
7
TheoremsnullMeasurableSet, nullMeasurableSet_biInter, nullMeasurableSet_biUnion, congr_ae, nullMeasurable, nullMeasurableSet, comp_nullMeasurable, out, out', ae_completion, coe_completion, isComplete, completion_apply, isComplete_iff, measurable', measurable_of_complete, biInter, biUnion, compl, compl_iff, compl_toMeasurable_compl_ae_eq, const, diff, disjointed, exists_measurable_subset_ae_eq, exists_measurable_superset_ae_eq, iInter, iUnion, insert, instMeasurableSingletonClass, inter, measurable_of_complete, of_compl, of_null, of_subsingleton, sInter, sUnion, symmDiff, toMeasurable_ae_eq, union, union_null, instSubsingleton, exists_subordinate_pairwise_disjoint, measurableSet_of_null, measure_add_measure_complβ‚€, measure_diff_symm, measure_iUnion, measure_iUnionβ‚€, measure_inter_add_diffβ‚€, measure_of_measure_compl_eq_zero, measure_preimage_fst_singleton_eq_sum, measure_preimage_fst_singleton_eq_tsum, measure_preimage_snd_singleton_eq_sum, measure_preimage_snd_singleton_eq_tsum, measure_union_add_interβ‚€, measure_union_add_interβ‚€', measure_unionβ‚€, measure_unionβ‚€', measure_unionβ‚€_aux, nullMeasurableSet_empty, nullMeasurableSet_eq, nullMeasurableSet_insert, nullMeasurableSet_singleton, nullMeasurableSet_toMeasurable, nullMeasurableSet_univ, nullMeasurableSet, nullMeasurableSet_biInter, nullMeasurableSet_biUnion, nullMeasurableSet_sInter, nullMeasurableSet_sUnion
70
Total77

Finset

Theorems

NameKindAssumesProvesValidatesDepends On
nullMeasurableSet πŸ“–mathematicalβ€”MeasureTheory.NullMeasurableSet
SetLike.coe
Finset
instSetLike
β€”measurableSet
nullMeasurableSet_biInter πŸ“–mathematicalMeasureTheory.NullMeasurableSetSet.iInter
Finset
instMembership
β€”Set.Finite.nullMeasurableSet_biInter
finite_toSet
nullMeasurableSet_biUnion πŸ“–mathematicalMeasureTheory.NullMeasurableSetSet.iUnion
Finset
instMembership
β€”measurableSet_biUnion

Measurable

Theorems

NameKindAssumesProvesValidatesDepends On
congr_ae πŸ“–β€”Measurable
Filter.EventuallyEq
MeasureTheory.ae
MeasureTheory.Measure
MeasureTheory.Measure.instFunLike
MeasureTheory.Measure.instOuterMeasureClass
β€”β€”MeasureTheory.Measure.instOuterMeasureClass
MeasureTheory.NullMeasurable.measurable_of_complete
MeasureTheory.NullMeasurable.congr
nullMeasurable
nullMeasurable πŸ“–mathematicalMeasurableMeasureTheory.NullMeasurableβ€”eventuallyMeasurable
MeasureTheory.Measure.instOuterMeasureClass

MeasurableSet

Theorems

NameKindAssumesProvesValidatesDepends On
nullMeasurableSet πŸ“–mathematicalMeasurableSetMeasureTheory.NullMeasurableSetβ€”eventuallyMeasurableSet
MeasureTheory.Measure.instOuterMeasureClass

MeasureTheory

Definitions

NameCategoryTheorems
NullMeasurable πŸ“–MathDef
5 mathmath: AEMeasurable.nullMeasurable, Measure.nullMeasurable_comp_snd, Measurable.nullMeasurable, aestronglyMeasurable_iff_nullMeasurable_separable, Measure.nullMeasurable_comp_fst
NullMeasurableSet πŸ“–MathDef
50 mathmath: NullMeasurableSet.of_null, nullMeasurableSet_Ioc, nullMeasurableSet_Icc, nullMeasurableSet_Ioo, NullMeasurableSet.const, IsFundamentalDomain.nullMeasurableSet_smul, nullMeasurableSet_Ioi, Set.OrdConnected.nullMeasurableSet, nullMeasurableSet_singleton, Measure.nullMeasurableSet_prod, Measure.nullMeasurableSet_preimage_fst, MeasurableSet.nullMeasurableSet, IsAddFundamentalDomain.nullMeasurableSet_vadd, AEStronglyMeasurable.nullMeasurableSet_support, nullMeasurableSet_empty, IsAddFundamentalDomain.nullMeasurableSet, nullMeasurableSet_le, IsOpen.nullMeasurableSet, nullMeasurableSet_smul_measure_iff, AEStronglyMeasurable.nullMeasurableSet_mulSupport, AEMeasurable.nullMeasurableSet_preimage, nullMeasurableSet_Ici, nullMeasurableSet_univ, Measure.nullMeasurableSet_prod_of_ne_zero, Set.Finite.nullMeasurableSet, AEStronglyMeasurable.nullMeasurableSet_le, nullMeasurableSet_lt', IsFundamentalDomain.nullMeasurableSet, nullMeasurableSet_toMeasurable, NullMeasurableSet.of_subsingleton, NullMeasurableSet.compl_iff, IsClosed.nullMeasurableSet, nullMeasurableSet_Iio, Measure.nullMeasurableSet_support, nullMeasurableSet_eq, nullMeasurableSet_of_null_frontier, nullMeasurableSet_eq_fun, Convex.nullMeasurableSet, aemeasurable_indicator_const_iff, Measure.nullMeasurableSet_compl_support, nullMeasurableSet_Ico, nullMeasurableSet_restrict_of_subset, Measure.nullMeasurableSet_preimage_snd, AEStronglyMeasurable.nullMeasurableSet_eq_fun, Finset.nullMeasurableSet, nullMeasurableSet_lt, nullMeasurableSet_insert, IsCompact.nullMeasurableSet, nullMeasurableSet_Iic, AEStronglyMeasurable.nullMeasurableSet_lt
NullMeasurableSpace πŸ“–CompOp
9 mathmath: Measure.MeasureDense.completion, NullMeasurable.measurable', NullMeasurableSpace.instSubsingleton, Measure.completion.isComplete, Measure.ae_completion, instIsSeparableNullMeasurableSpaceCompletion, Measure.completion_apply, Measure.coe_completion, NullMeasurableSet.instMeasurableSingletonClass

Theorems

NameKindAssumesProvesValidatesDepends On
exists_subordinate_pairwise_disjoint πŸ“–mathematicalNullMeasurableSet
Pairwise
Function.onFun
Set
AEDisjoint
Set.instHasSubset
Filter.EventuallyEq
ae
Measure
Measure.instFunLike
Measure.instOuterMeasureClass
MeasurableSet
Disjoint
OmegaCompletePartialOrder.toPartialOrder
CompleteLattice.instOmegaCompletePartialOrder
CompleteBooleanAlgebra.toCompleteLattice
CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra
Set.instCompleteAtomicBooleanAlgebra
HeytingAlgebra.toOrderBot
Order.Frame.toHeytingAlgebra
CompleteDistribLattice.toFrame
CompleteBooleanAlgebra.toCompleteDistribLattice
β€”Measure.instOuterMeasureClass
exists_null_pairwise_disjoint_diff
HasSubset.Subset.trans
Set.instIsTransSubset
Set.diff_subset
Filter.EventuallyEq.trans
Filter.EventuallyEq.symm
diff_null_ae_eq_self
MeasurableSet.diff
Pairwise.mono
Disjoint.mono
Set.diff_subset_diff_left
NullMeasurableSet.exists_measurable_subset_ae_eq
measurableSet_of_null πŸ“–mathematicalDFunLike.coe
Measure
Set
ENNReal
Measure.instFunLike
instZeroENNReal
MeasurableSetβ€”Measure.IsComplete.out'
measure_add_measure_complβ‚€ πŸ“–mathematicalNullMeasurableSetENNReal
Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
ENNReal.instCommSemiring
DFunLike.coe
Measure
Set
Measure.instFunLike
Compl.compl
Set.instCompl
Set.univ
β€”measure_unionβ‚€'
aedisjoint_compl_right
Set.union_compl_self
measure_diff_symm πŸ“–mathematicalNullMeasurableSet
DFunLike.coe
Measure
Set
ENNReal
Measure.instFunLike
Set.instSDiffβ€”measure_inter_add_diffβ‚€
Set.inter_comm
measure_iUnion πŸ“–mathematicalPairwise
Function.onFun
Set
Disjoint
OmegaCompletePartialOrder.toPartialOrder
CompleteLattice.instOmegaCompletePartialOrder
CompleteBooleanAlgebra.toCompleteLattice
CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra
Set.instCompleteAtomicBooleanAlgebra
HeytingAlgebra.toOrderBot
Order.Frame.toHeytingAlgebra
CompleteDistribLattice.toFrame
CompleteBooleanAlgebra.toCompleteDistribLattice
MeasurableSet
DFunLike.coe
Measure
ENNReal
Measure.instFunLike
Set.iUnion
tsum
ENNReal.instAddCommMonoid
ENNReal.instTopologicalSpace
SummationFilter.unconditional
β€”measure_eq_extend
MeasurableSet.iUnion
extend_iUnion
MeasurableSet.empty
OuterMeasure.empty
instCountableNat
Measure.m_iUnion
measure_iUnionβ‚€ πŸ“–mathematicalPairwise
Function.onFun
Set
AEDisjoint
NullMeasurableSet
DFunLike.coe
Measure
ENNReal
Measure.instFunLike
Set.iUnion
tsum
ENNReal.instAddCommMonoid
ENNReal.instTopologicalSpace
SummationFilter.unconditional
β€”Measure.instOuterMeasureClass
exists_subordinate_pairwise_disjoint
measure_congr
EventuallyEq.countable_iUnion
instCountableInterFilter
measure_iUnion
tsum_congr
Filter.EventuallyEq.symm
measure_inter_add_diffβ‚€ πŸ“–mathematicalNullMeasurableSetENNReal
Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
ENNReal.instCommSemiring
DFunLike.coe
Measure
Set
Measure.instFunLike
Set.instInter
Set.instSDiff
β€”le_antisymm
exists_measurable_superset
MeasurableSet.nullMeasurableSet
add_le_add
IsOrderedAddMonoid.toAddLeftMono
ENNReal.instIsOrderedAddMonoid
covariant_swap_add_of_covariant_add
measure_mono
Measure.instOuterMeasureClass
Set.inter_subset_inter
subset_refl
Set.instReflSubset
Set.diff_subset_diff
measure_unionβ‚€_aux
NullMeasurableSet.inter
NullMeasurableSet.diff
Disjoint.aedisjoint
disjoint_inf_sdiff
Set.inter_union_diff
measure_le_inter_add_diff
measure_of_measure_compl_eq_zero πŸ“–mathematicalDFunLike.coe
Measure
Set
ENNReal
Measure.instFunLike
Compl.compl
Set.instCompl
instZeroENNReal
Set.univβ€”add_zero
measure_add_measure_complβ‚€
NullMeasurableSet.of_compl
NullMeasurableSet.of_null
measure_preimage_fst_singleton_eq_sum πŸ“–mathematicalβ€”DFunLike.coe
Measure
Prod.instMeasurableSpace
Set
ENNReal
Measure.instFunLike
Set.preimage
Set.instSingletonSet
Finset.sum
ENNReal.instAddCommMonoid
Finset.univ
β€”measure_preimage_fst_singleton_eq_tsum
Finite.to_countable
Finite.of_fintype
tsum_fintype
SummationFilter.instLeAtTopUnconditional
measure_preimage_fst_singleton_eq_tsum πŸ“–mathematicalβ€”DFunLike.coe
Measure
Prod.instMeasurableSpace
Set
ENNReal
Measure.instFunLike
Set.preimage
Set.instSingletonSet
tsum
ENNReal.instAddCommMonoid
ENNReal.instTopologicalSpace
SummationFilter.unconditional
β€”measure_iUnion
MeasurableSet.singleton
Prod.instMeasurableSingletonClass
Set.iUnion_singleton_eq_range
Set.preimage_fst_singleton_eq_range
measure_preimage_snd_singleton_eq_sum πŸ“–mathematicalβ€”DFunLike.coe
Measure
Prod.instMeasurableSpace
Set
ENNReal
Measure.instFunLike
Set.preimage
Set.instSingletonSet
Finset.sum
ENNReal.instAddCommMonoid
Finset.univ
β€”measure_preimage_snd_singleton_eq_tsum
Finite.to_countable
Finite.of_fintype
tsum_fintype
SummationFilter.instLeAtTopUnconditional
measure_preimage_snd_singleton_eq_tsum πŸ“–mathematicalβ€”DFunLike.coe
Measure
Prod.instMeasurableSpace
Set
ENNReal
Measure.instFunLike
Set.preimage
Set.instSingletonSet
tsum
ENNReal.instAddCommMonoid
ENNReal.instTopologicalSpace
SummationFilter.unconditional
β€”Set.ext
Set.iUnion_singleton_eq_range
measure_iUnion
Prod.instMeasurableSingletonClass
measure_union_add_interβ‚€ πŸ“–mathematicalNullMeasurableSetENNReal
Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
ENNReal.instCommSemiring
DFunLike.coe
Measure
Set
Measure.instFunLike
Set.instUnion
Set.instInter
β€”measure_inter_add_diffβ‚€
Set.union_inter_cancel_right
Set.union_diff_right
add_comm
add_assoc
add_right_comm
measure_union_add_interβ‚€' πŸ“–mathematicalNullMeasurableSetENNReal
Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
ENNReal.instCommSemiring
DFunLike.coe
Measure
Set
Measure.instFunLike
Set.instUnion
Set.instInter
β€”Set.union_comm
Set.inter_comm
measure_union_add_interβ‚€
add_comm
measure_unionβ‚€ πŸ“–mathematicalNullMeasurableSet
AEDisjoint
DFunLike.coe
Measure
Set
ENNReal
Measure.instFunLike
Set.instUnion
Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
ENNReal.instCommSemiring
β€”measure_union_add_interβ‚€
add_zero
measure_unionβ‚€' πŸ“–mathematicalNullMeasurableSet
AEDisjoint
DFunLike.coe
Measure
Set
ENNReal
Measure.instFunLike
Set.instUnion
Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
ENNReal.instCommSemiring
β€”Set.union_comm
measure_unionβ‚€
AEDisjoint.symm
add_comm
measure_unionβ‚€_aux πŸ“–mathematicalNullMeasurableSet
AEDisjoint
DFunLike.coe
Measure
Set
ENNReal
Measure.instFunLike
Set.instUnion
Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
ENNReal.instCommSemiring
β€”Set.union_eq_iUnion
measure_iUnionβ‚€
Bool.countable
pairwise_on_bool
AEDisjoint.symmetric
tsum_fintype
SummationFilter.instLeAtTopUnconditional
Fintype.sum_bool
nullMeasurableSet_empty πŸ“–mathematicalβ€”NullMeasurableSet
Set
Set.instEmptyCollection
β€”MeasurableSet.empty
nullMeasurableSet_eq πŸ“–mathematicalβ€”NullMeasurableSet
setOf
β€”nullMeasurableSet_singleton
nullMeasurableSet_insert πŸ“–mathematicalβ€”NullMeasurableSet
Set
Set.instInsert
β€”measurableSet_insert
nullMeasurableSet_singleton πŸ“–mathematicalβ€”NullMeasurableSet
Set
Set.instSingletonSet
β€”MeasurableSingletonClass.measurableSet_singleton
nullMeasurableSet_toMeasurable πŸ“–mathematicalβ€”NullMeasurableSet
toMeasurable
β€”MeasurableSet.nullMeasurableSet
measurableSet_toMeasurable
nullMeasurableSet_univ πŸ“–mathematicalβ€”NullMeasurableSet
Set.univ
β€”MeasurableSet.univ

MeasureTheory.Measurable

Theorems

NameKindAssumesProvesValidatesDepends On
comp_nullMeasurable πŸ“–β€”Measurable
MeasureTheory.NullMeasurable
β€”β€”Measurable.comp_eventuallyMeasurable
MeasureTheory.Measure.instOuterMeasureClass

MeasureTheory.Measure

Definitions

NameCategoryTheorems
IsComplete πŸ“–CompData
2 mathmath: completion.isComplete, isComplete_iff
completion πŸ“–CompOp
6 mathmath: MeasureDense.completion, completion.isComplete, ae_completion, MeasureTheory.instIsSeparableNullMeasurableSpaceCompletion, completion_apply, coe_completion

Theorems

NameKindAssumesProvesValidatesDepends On
ae_completion πŸ“–mathematicalβ€”MeasureTheory.ae
MeasureTheory.NullMeasurableSpace
MeasureTheory.Measure
MeasureTheory.NullMeasurableSpace.instMeasurableSpace
instFunLike
instOuterMeasureClass
completion
β€”instOuterMeasureClass
coe_completion πŸ“–mathematicalβ€”DFunLike.coe
MeasureTheory.Measure
MeasureTheory.NullMeasurableSpace
MeasureTheory.NullMeasurableSpace.instMeasurableSpace
Set
ENNReal
instFunLike
completion
β€”β€”
completion_apply πŸ“–mathematicalβ€”DFunLike.coe
MeasureTheory.Measure
MeasureTheory.NullMeasurableSpace
MeasureTheory.NullMeasurableSpace.instMeasurableSpace
Set
ENNReal
instFunLike
completion
β€”β€”
isComplete_iff πŸ“–mathematicalβ€”IsComplete
MeasurableSet
β€”IsComplete.out'

MeasureTheory.Measure.IsComplete

Theorems

NameKindAssumesProvesValidatesDepends On
out πŸ“–mathematicalDFunLike.coe
MeasureTheory.Measure
Set
ENNReal
MeasureTheory.Measure.instFunLike
instZeroENNReal
MeasurableSetβ€”out'
out' πŸ“–mathematicalDFunLike.coe
MeasureTheory.Measure
Set
ENNReal
MeasureTheory.Measure.instFunLike
instZeroENNReal
MeasurableSetβ€”β€”

MeasureTheory.Measure.completion

Theorems

NameKindAssumesProvesValidatesDepends On
isComplete πŸ“–mathematicalβ€”MeasureTheory.Measure.IsComplete
MeasureTheory.NullMeasurableSpace
MeasureTheory.NullMeasurableSpace.instMeasurableSpace
MeasureTheory.Measure.completion
β€”MeasureTheory.NullMeasurableSet.of_null

MeasureTheory.NullMeasurable

Theorems

NameKindAssumesProvesValidatesDepends On
measurable' πŸ“–mathematicalMeasureTheory.NullMeasurableMeasurable
MeasureTheory.NullMeasurableSpace
MeasureTheory.NullMeasurableSpace.instMeasurableSpace
β€”β€”
measurable_of_complete πŸ“–mathematicalMeasureTheory.NullMeasurableMeasurableβ€”MeasureTheory.NullMeasurableSet.measurable_of_complete

MeasureTheory.NullMeasurableSet

Theorems

NameKindAssumesProvesValidatesDepends On
biInter πŸ“–mathematicalMeasureTheory.NullMeasurableSetSet.iInter
Set
Set.instMembership
β€”MeasurableSet.biInter
biUnion πŸ“–mathematicalMeasureTheory.NullMeasurableSetSet.iUnion
Set
Set.instMembership
β€”MeasurableSet.biUnion
compl πŸ“–mathematicalMeasureTheory.NullMeasurableSetCompl.compl
Set
Set.instCompl
β€”MeasurableSet.compl
compl_iff πŸ“–mathematicalβ€”MeasureTheory.NullMeasurableSet
Compl.compl
Set
Set.instCompl
β€”MeasurableSet.compl_iff
compl_toMeasurable_compl_ae_eq πŸ“–mathematicalMeasureTheory.NullMeasurableSetFilter.EventuallyEq
MeasureTheory.ae
MeasureTheory.Measure
MeasureTheory.Measure.instFunLike
MeasureTheory.Measure.instOuterMeasureClass
Compl.compl
Pi.instCompl
Prop.instCompl
MeasureTheory.toMeasurable
Set
Set.instCompl
β€”MeasureTheory.Measure.instOuterMeasureClass
MeasureTheory.ae_eq_set_compl
toMeasurable_ae_eq
compl
const πŸ“–mathematicalβ€”MeasureTheory.NullMeasurableSet
setOf
β€”MeasurableSet.const
diff πŸ“–mathematicalMeasureTheory.NullMeasurableSetSet
Set.instSDiff
β€”MeasurableSet.diff
disjointed πŸ“–mathematicalMeasureTheory.NullMeasurableSetdisjointed
Set
BooleanAlgebra.toGeneralizedBooleanAlgebra
Set.instBooleanAlgebra
Nat.instPreorder
LocallyFiniteOrder.toLocallyFiniteOrderBot
Nat.instOrderBot
Nat.instLocallyFiniteOrder
β€”MeasurableSet.disjointed
exists_measurable_subset_ae_eq πŸ“–mathematicalMeasureTheory.NullMeasurableSetSet
Set.instHasSubset
MeasurableSet
Filter.EventuallyEq
MeasureTheory.ae
MeasureTheory.Measure
MeasureTheory.Measure.instFunLike
MeasureTheory.Measure.instOuterMeasureClass
β€”MeasureTheory.Measure.instOuterMeasureClass
Set.compl_subset_comm
MeasureTheory.subset_toMeasurable
MeasurableSet.compl
MeasureTheory.measurableSet_toMeasurable
compl_toMeasurable_compl_ae_eq
exists_measurable_superset_ae_eq πŸ“–mathematicalMeasureTheory.NullMeasurableSetSet
Set.instHasSubset
MeasurableSet
Filter.EventuallyEq
MeasureTheory.ae
MeasureTheory.Measure
MeasureTheory.Measure.instFunLike
MeasureTheory.Measure.instOuterMeasureClass
β€”MeasureTheory.Measure.instOuterMeasureClass
Set.diff_subset_iff
MeasureTheory.subset_toMeasurable
MeasurableSet.union
MeasureTheory.measurableSet_toMeasurable
MeasureTheory.measure_toMeasurable
MeasureTheory.ae_le_set
Filter.EventuallyEq.le
Set.union_empty
Filter.EventuallyEq.union
Filter.EventuallyEq.symm
iInter πŸ“–mathematicalMeasureTheory.NullMeasurableSetSet.iInterβ€”MeasurableSet.iInter
iUnion πŸ“–mathematicalMeasureTheory.NullMeasurableSetSet.iUnionβ€”MeasurableSet.iUnion
insert πŸ“–mathematicalMeasureTheory.NullMeasurableSetSet
Set.instInsert
β€”MeasurableSet.insert
instMeasurableSingletonClass πŸ“–mathematicalβ€”MeasurableSingletonClass
MeasureTheory.NullMeasurableSpace
MeasureTheory.NullMeasurableSpace.instMeasurableSpace
β€”eventuallyMeasurableSingleton
MeasureTheory.Measure.instOuterMeasureClass
inter πŸ“–mathematicalMeasureTheory.NullMeasurableSetSet
Set.instInter
β€”MeasurableSet.inter
measurable_of_complete πŸ“–mathematicalMeasureTheory.NullMeasurableSetMeasurableSetβ€”MeasurableSet.diff
MeasureTheory.measurableSet_toMeasurable
MeasureTheory.measurableSet_of_null
MeasureTheory.Measure.instOuterMeasureClass
MeasureTheory.ae_le_set
Filter.EventuallyEq.le
toMeasurable_ae_eq
Set.diff_diff_cancel_left
MeasureTheory.subset_toMeasurable
of_compl πŸ“–β€”MeasureTheory.NullMeasurableSet
Compl.compl
Set
Set.instCompl
β€”β€”MeasurableSet.of_compl
of_null πŸ“–mathematicalDFunLike.coe
MeasureTheory.Measure
Set
ENNReal
MeasureTheory.Measure.instFunLike
instZeroENNReal
MeasureTheory.NullMeasurableSetβ€”MeasureTheory.Measure.instOuterMeasureClass
MeasurableSet.empty
MeasureTheory.ae_eq_empty
of_subsingleton πŸ“–mathematicalβ€”MeasureTheory.NullMeasurableSetβ€”Subsingleton.measurableSet
MeasureTheory.NullMeasurableSpace.instSubsingleton
sInter πŸ“–mathematicalMeasureTheory.NullMeasurableSetSet.sInterβ€”MeasurableSet.sInter
sUnion πŸ“–mathematicalMeasureTheory.NullMeasurableSetSet.sUnionβ€”Set.sUnion_eq_biUnion
MeasurableSet.biUnion
symmDiff πŸ“–mathematicalMeasureTheory.NullMeasurableSetsymmDiff
Set
SemilatticeSup.toMax
Lattice.toSemilatticeSup
ConditionallyCompleteLattice.toLattice
CompleteLattice.toConditionallyCompleteLattice
CompleteBooleanAlgebra.toCompleteLattice
CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra
Set.instCompleteAtomicBooleanAlgebra
Set.instSDiff
β€”union
diff
toMeasurable_ae_eq πŸ“–mathematicalMeasureTheory.NullMeasurableSetFilter.EventuallyEq
MeasureTheory.ae
MeasureTheory.Measure
MeasureTheory.Measure.instFunLike
MeasureTheory.Measure.instOuterMeasureClass
MeasureTheory.toMeasurable
β€”MeasureTheory.Measure.instOuterMeasureClass
MeasureTheory.exists_measurable_superset
MeasureTheory.toMeasurable_def
exists_measurable_superset_ae_eq
union πŸ“–mathematicalMeasureTheory.NullMeasurableSetSet
Set.instUnion
β€”MeasurableSet.union
union_null πŸ“–mathematicalMeasureTheory.NullMeasurableSet
DFunLike.coe
MeasureTheory.Measure
Set
ENNReal
MeasureTheory.Measure.instFunLike
instZeroENNReal
Set.instUnionβ€”union
of_null

MeasureTheory.NullMeasurableSpace

Definitions

NameCategoryTheorems
instInhabited πŸ“–CompOpβ€”
instMeasurableSpace πŸ“–CompOp
8 mathmath: MeasureTheory.Measure.MeasureDense.completion, MeasureTheory.NullMeasurable.measurable', MeasureTheory.Measure.completion.isComplete, MeasureTheory.Measure.ae_completion, MeasureTheory.instIsSeparableNullMeasurableSpaceCompletion, MeasureTheory.Measure.completion_apply, MeasureTheory.Measure.coe_completion, MeasureTheory.NullMeasurableSet.instMeasurableSingletonClass

Theorems

NameKindAssumesProvesValidatesDepends On
instSubsingleton πŸ“–mathematicalβ€”MeasureTheory.NullMeasurableSpaceβ€”β€”

Set.Finite

Theorems

NameKindAssumesProvesValidatesDepends On
nullMeasurableSet πŸ“–mathematicalβ€”MeasureTheory.NullMeasurableSetβ€”measurableSet
nullMeasurableSet_biInter πŸ“–mathematicalMeasureTheory.NullMeasurableSetSet.iInter
Set
Set.instMembership
β€”measurableSet_biInter
nullMeasurableSet_biUnion πŸ“–mathematicalMeasureTheory.NullMeasurableSetSet.iUnion
Set
Set.instMembership
β€”measurableSet_biUnion
nullMeasurableSet_sInter πŸ“–mathematicalMeasureTheory.NullMeasurableSetSet.sInterβ€”MeasureTheory.NullMeasurableSet.sInter
countable
nullMeasurableSet_sUnion πŸ“–mathematicalMeasureTheory.NullMeasurableSetSet.sUnionβ€”measurableSet_sUnion

---

← Back to Index