Theorems · Theorem · measure theory

MeasureTheory.HaveLebesgueDecomposition.mconv

∀ {G : Type u_3} [inst : Group G] {mG : MeasurableSpace G} [MeasurableMul₂ G] [MeasurableInv G]
  {μ : MeasureTheory.Measure G} [μ.IsMulLeftInvariant] [MeasureTheory.SFinite μ] {ν₁ ν₂ : MeasureTheory.Measure G}
  [ν₁.HaveLebesgueDecomposition μ] [ν₂.HaveLebesgueDecomposition μ],
  ν₁.AbsolutelyContinuous μ → ν₂.AbsolutelyContinuous μ → (ν₁.mconv ν₂).HaveLebesgueDecomposition μ

Defined in

Mathlib.MeasureTheory.Measure.Decomposition.RadonNikodym

Cited by

2 results in Mathlib

Foundations

Depth 233 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

GroupMeasurableMul₂MeasurableInvMeasureTheory.Measure.IsMulLeftInvariantMeasureTheory.SFiniteMeasureTheory.Measure.HaveLebesgueDecompositionMeasureTheory.Measure.HaveLebesgueDecomposition