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Theorems · Theorem · measure theory

MeasureTheory.SignedMeasure.rnDeriv_neg

∀ {α : Type u_1} {m : MeasurableSpace α} (s : MeasureTheory.SignedMeasure α) (μ : MeasureTheory.Measure α)
  [s.HaveLebesgueDecomposition μ], (-s).rnDeriv μ =ᵐ[μ] -s.rnDeriv μ
Defined in
Mathlib.MeasureTheory.VectorMeasure.Decomposition.Lebesgue
Cited by
1 results in Mathlib
Foundations
Depth 266 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
MeasureTheory.SignedMeasure.HaveLebesgueDecomposition
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Around this declaration

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

MeasureTheory.SignedMeasure.rnDeriv_sub · cited by 0SignedMeasure.rnDeriv_subReal · cited by 25697RealMeasurableSpace · cited by 13106MeasurableSpaceMeasureTheory.Measure · cited by 10939MeasureTheory.MeasureMeasureTheory.ae · cited by 2352MeasureTheory.aeFilter.EventuallyEq · cited by 1912Filter.EventuallyEqMeasureTheory.VectorMeasure · cited by 451MeasureTheory.VectorMeasu…MeasureTheory.SignedMeasure · cited by 108MeasureTheory.SignedMeasu…add_right_inj · cited by 71add_right_injneg_add · cited by 69neg_addMeasureTheory.Integrable.neg · cited by 40Integrable.negMeasureTheory.Measure.withDensityᵥ · cited by 36Measure.withDensityᵥMeasureTheory.SignedMeasure.rnDeriv · cited by 13SignedMeasure.rnDerivMeasureTheory.SignedMeasure.singularPart · cited by 13SignedMeasure.singularPartMeasureTheory.SignedMeasure.HaveLebesgueDecomposition · cited by 10SignedMeasure.HaveLebesgu…MeasureTheory.SignedMeasure.integrable_rnDeriv · cited by 9SignedMeasure.integrable_…SignedMeasure.rnDeriv_negCITED BYCITES

Cites19

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Cited by1

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