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Theorems · Theorem · measure theory

MeasureTheory.SignedMeasure.totalVariation_mutuallySingular_iff

∀ {α : Type u_1} [inst : MeasurableSpace α] (s : MeasureTheory.SignedMeasure α) (μ : MeasureTheory.Measure α),
  s.totalVariation.MutuallySingular μ ↔
    s.toJordanDecomposition.posPart.MutuallySingular μ ∧ s.toJordanDecomposition.negPart.MutuallySingular μ
Defined in
Mathlib.MeasureTheory.VectorMeasure.Decomposition.Jordan
Cited by
1 results in Mathlib
Foundations
Depth 197 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
MeasurableSpace
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Around this declaration

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

MeasureTheory.SignedMeasure.jordanDecomposition_add_withDensity_mutuallySingular · cited by 1SignedMeasure.jordanDecom…MeasurableSpace · cited by 13106MeasurableSpaceMeasureTheory.Measure · cited by 10939MeasureTheory.MeasureMeasureTheory.SignedMeasure · cited by 108MeasureTheory.SignedMeasu…MeasureTheory.Measure.MutuallySingular · cited by 91Measure.MutuallySingularMeasureTheory.JordanDecomposition.negPart · cited by 44JordanDecomposition.negPa…MeasureTheory.JordanDecomposition.posPart · cited by 43JordanDecomposition.posPa…MeasureTheory.SignedMeasure.toJordanDecomposition · cited by 34SignedMeasure.toJordanDec…MeasureTheory.SignedMeasure.totalVariation · cited by 13SignedMeasure.totalVariat…MeasureTheory.Measure.MutuallySingular.add_left_iff · cited by 6MutuallySingular.add_left…SignedMeasure.totalVariation_…CITED BYCITES

Cites9

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Cited by1

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