Theorems · Theorem · measure theory

MeasureTheory.Measure.rnDeriv_add_right_of_absolutelyContinuous_of_mutuallySingular

∀ {α : Type u_1} {m : MeasurableSpace α} {μ ν ν' : MeasureTheory.Measure α} [μ.HaveLebesgueDecomposition ν]
  [μ.HaveLebesgueDecomposition (ν + ν')] [MeasureTheory.SigmaFinite ν],
  μ.AbsolutelyContinuous ν → ν.MutuallySingular ν' → μ.rnDeriv (ν + ν') =ᵐ[ν] μ.rnDeriv ν

Auxiliary lemma for rnDeriv_add_right_of_mutuallySingular.

Defined in

Mathlib.MeasureTheory.Measure.Decomposition.RadonNikodym

Cited by

1 results in Mathlib

Foundations

Depth 215 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

MeasureTheory.Measure.HaveLebesgueDecompositionMeasureTheory.Measure.HaveLebesgueDecompositionMeasureTheory.SigmaFinite