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Theorems · Theorem · measure theory

MeasureTheory.SignedMeasure.rnDeriv_add

∀ {α : Type u_1} {m : MeasurableSpace α} (s t : MeasureTheory.SignedMeasure α) (μ : MeasureTheory.Measure α)
  [s.HaveLebesgueDecomposition μ] [t.HaveLebesgueDecomposition μ] [(s + t).HaveLebesgueDecomposition μ],
  (s + t).rnDeriv μ =ᵐ[μ] s.rnDeriv μ + t.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.HaveLebesgueDecompositionMeasureTheory.SignedMeasure.HaveLebesgueDecompositionMeasureTheory.SignedMeasure.HaveLebesgueDecomposition
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Around this declaration

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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.EventuallyEqadd_comm · cited by 1535add_commadd_assoc · cited by 746add_assocMeasureTheory.VectorMeasure · cited by 451MeasureTheory.VectorMeasu…MeasureTheory.SignedMeasure · cited by 108MeasureTheory.SignedMeasu…add_right_inj · cited by 71add_right_injMeasureTheory.Integrable.add · cited by 42Integrable.addMeasureTheory.Measure.withDensityᵥ · cited by 36Measure.withDensityᵥMeasureTheory.SignedMeasure.rnDeriv · cited by 13SignedMeasure.rnDerivMeasureTheory.SignedMeasure.singularPart · cited by 13SignedMeasure.singularPartMeasureTheory.SignedMeasure.HaveLebesgueDecomposition · cited by 10SignedMeasure.HaveLebesgu…SignedMeasure.rnDeriv_addCITED BYCITES

Cites20

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Cited by1

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