Theorems · Theorem · measure theory
MeasureTheory.SignedMeasure.absolutelyContinuous_ennreal_iff
∀ {α : Type u_1} [inst : MeasurableSpace α] (s : MeasureTheory.SignedMeasure α)
(μ : MeasureTheory.VectorMeasure α ENNReal),
MeasureTheory.VectorMeasure.AbsolutelyContinuous s μ ↔ s.totalVariation.AbsolutelyContinuous μ.ennrealToMeasure- Cited by
- 1 results in Mathlib
- Foundations
- Depth 179 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- MeasurableSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites42
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Setproof · cited by 53,352
- Realstatement · cited by 25,697
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measureproof · cited by 10,939
- ENNRealstatement and proof · cited by 9,879
- MeasurableSetproof · cited by 3,075
- Compl.complproof · cited by 2,925
- add_zeroproof · cited by 2,707
- ENNReal.ofNNRealproof · cited by 1,279
- neg_zeroproof · cited by 542
- MeasureTheory.VectorMeasurestatement and proof · cited by 451
Cited by1
Results whose statement or proof uses this declaration.
- MeasureTheory.SignedMeasure.withDensityᵥ_rnDeriv_eqproof · cited by 2