Theorems · Theorem · measure theory
MeasureTheory.SignedMeasure.totalVariation_absolutelyContinuous_iff
∀ {α : Type u_1} [inst : MeasurableSpace α] (s : MeasureTheory.SignedMeasure α) (μ : MeasureTheory.Measure α),
s.totalVariation.AbsolutelyContinuous μ ↔
s.toJordanDecomposition.posPart.AbsolutelyContinuous μ ∧ s.toJordanDecomposition.negPart.AbsolutelyContinuous μ- Cited by
- 1 results in Mathlib
- Foundations
- Depth 178 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.
Cites16
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
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement and proof · cited by 10,939
- ENNRealproof · cited by 9,879
- MeasurableSetproof · cited by 3,075
- add_zeroproof · cited by 2,707
- MeasureTheory.Measure.AbsolutelyContinuousstatement and proof · cited by 325
- MeasureTheory.SignedMeasurestatement and proof · cited by 108
- MeasureTheory.JordanDecomposition.negPartstatement and proof · cited by 44
- MeasureTheory.JordanDecomposition.posPartstatement and proof · cited by 43
- MeasureTheory.Measure.AbsolutelyContinuous.mkproof · cited by 38
Cited by1
Results whose statement or proof uses this declaration.
- MeasureTheory.SignedMeasure.withDensityᵥ_rnDeriv_eqproof · cited by 2