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Theorems · Theorem · measure theory

MeasureTheory.Measure.rnDeriv_add_right_of_mutuallySingular

∀ {α : Type u_1} {m : MeasurableSpace α} {μ ν ν' : MeasureTheory.Measure α} [MeasureTheory.SigmaFinite μ]
  [MeasureTheory.SigmaFinite ν] [MeasureTheory.SigmaFinite ν'],
  ν.MutuallySingular ν' → μ.rnDeriv (ν + ν') =ᵐ[ν] μ.rnDeriv ν
Defined in
Mathlib.MeasureTheory.Measure.Decomposition.RadonNikodym
Cited by
1 results in Mathlib
Foundations
Depth 217 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
MeasureTheory.SigmaFiniteMeasureTheory.SigmaFiniteMeasureTheory.SigmaFinite
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Around this declaration

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MeasureTheory.Measure.rnDeriv_withDensity_rnDeriv · cited by 1Measure.rnDeriv_withDensi…MeasurableSpace · cited by 13106MeasurableSpaceMeasureTheory.Measure · cited by 10939MeasureTheory.MeasureENNReal · cited by 9879ENNRealSet.ofPred · cited by 6101Set.ofPredMeasureTheory.ae · cited by 2352MeasureTheory.aeFilter.EventuallyEq · cited by 1912Filter.EventuallyEqFilter.univ_mem' · cited by 1672Filter.univ_mem'Filter.mp_mem · cited by 1537Filter.mp_memMeasureTheory.SigmaFinite · cited by 526MeasureTheory.SigmaFiniteFilter.EventuallyEq.symm · cited by 408EventuallyEq.symmMeasureTheory.Measure.AbsolutelyContinuous · cited by 325Measure.AbsolutelyContinu…MeasureTheory.Measure.withDensity · cited by 265Measure.withDensityMeasureTheory.Measure.rnDeriv · cited by 234Measure.rnDerivFilter.EventuallyEq.trans · cited by 123EventuallyEq.transMeasureTheory.Measure.MutuallySingular · cited by 91Measure.MutuallySingularMeasure.rnDeriv_add_right_of_…CITED BYCITES

Cites28

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Cited by1

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