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Theorems · Theorem · measure theory

MeasureTheory.SignedMeasure.singularPart_neg

∀ {α : Type u_1} {m : MeasurableSpace α} (s : MeasureTheory.SignedMeasure α) (μ : MeasureTheory.Measure α),
  (-s).singularPart μ = -s.singularPart μ
Defined in
Mathlib.MeasureTheory.VectorMeasure.Decomposition.Lebesgue
Cited by
2 results in Mathlib
Foundations
Depth 215 from the axioms · uses propext, Classical.choice, Quot.sound
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MeasureTheory.SignedMeasure.rnDeriv_neg · cited by 1SignedMeasure.rnDeriv_negMeasureTheory.SignedMeasure.singularPart_sub · cited by 0SignedMeasure.singularPar…Real · cited by 25697RealMeasurableSpace · cited by 13106MeasurableSpaceMeasureTheory.Measure · cited by 10939MeasureTheory.Measureneg_sub · cited by 272neg_subMeasureTheory.SignedMeasure · cited by 108MeasureTheory.SignedMeasu…MeasureTheory.Measure.singularPart · cited by 71Measure.singularPartMeasureTheory.JordanDecomposition.negPart · cited by 44JordanDecomposition.negPa…MeasureTheory.JordanDecomposition.posPart · cited by 43JordanDecomposition.posPa…MeasureTheory.Measure.toSignedMeasure · cited by 36Measure.toSignedMeasureMeasureTheory.SignedMeasure.toJordanDecomposition · cited by 34SignedMeasure.toJordanDec…MeasureTheory.SignedMeasure.singularPart · cited by 13SignedMeasure.singularPartMeasureTheory.SignedMeasure.toJordanDecomposition_neg · cited by 3SignedMeasure.toJordanDec…MeasureTheory.Measure.toSignedMeasure.congr_simp · cited by 3toSignedMeasure.congr_simpSignedMeasure.singularPart_negCITED BYCITES

Cites13

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Cited by2

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