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Theorems · Theorem · measure theory

MeasureTheory.VectorMeasure.AbsolutelyContinuous.ennrealToMeasure

∀ {α : Type u_1} {m : MeasurableSpace α} {M : Type u_4} [inst : AddCommMonoid M] [inst_1 : TopologicalSpace M]
  {v : MeasureTheory.VectorMeasure α M} {μ : MeasureTheory.VectorMeasure α ENNReal},
  (∀ ⦃s : Set α⦄, μ.ennrealToMeasure s = 0 → v s = 0) ↔ v.AbsolutelyContinuous μ
Defined in
Mathlib.MeasureTheory.VectorMeasure.Basic
Cited by
1 results in Mathlib
Foundations
Depth 172 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
AddCommMonoidTopologicalSpace
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

MeasureTheory.SignedMeasure.absolutelyContinuous_ennreal_iff · cited by 1SignedMeasure.absolutelyC…DFunLike.coe · cited by 62936DFunLike.coeSet · cited by 53352SetTopologicalSpace · cited by 24529TopologicalSpaceMeasurableSpace · cited by 13106MeasurableSpaceAddCommMonoid · cited by 12281AddCommMonoidMeasureTheory.Measure · cited by 10939MeasureTheory.MeasureENNReal · cited by 9879ENNRealMeasurableSet · cited by 3075MeasurableSetMeasureTheory.VectorMeasure · cited by 451MeasureTheory.VectorMeasu…MeasureTheory.VectorMeasure.not_measurable · cited by 21VectorMeasure.not_measura…MeasureTheory.VectorMeasure.AbsolutelyContinuous · cited by 19VectorMeasure.AbsolutelyC…MeasureTheory.VectorMeasure.ennrealToMeasure · cited by 13VectorMeasure.ennrealToMe…MeasureTheory.VectorMeasure.ennrealToMeasure_apply · cited by 11VectorMeasure.ennrealToMe…MeasureTheory.VectorMeasure.AbsolutelyContinuous.mk · cited by 5AbsolutelyContinuous.mkAbsolutelyContinuous.ennrealT…CITED BYCITES

Cites14

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Cited by1

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