Theorems · Theorem · measure theory

MeasureTheory.Measure.inv_rnDeriv_aux

∀ {α : Type u_1} {m : MeasurableSpace α} {μ ν : MeasureTheory.Measure α} [μ.HaveLebesgueDecomposition ν]
  [ν.HaveLebesgueDecomposition μ] [MeasureTheory.SigmaFinite μ],
  μ.AbsolutelyContinuous ν → ν.AbsolutelyContinuous μ → (μ.rnDeriv ν)⁻¹ =ᵐ[μ] ν.rnDeriv μ

Auxiliary lemma for inv_rnDeriv.

Defined in

Mathlib.MeasureTheory.Measure.Decomposition.RadonNikodym

Cited by

1 results in Mathlib

Foundations

Depth 216 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

MeasureTheory.Measure.HaveLebesgueDecompositionMeasureTheory.Measure.HaveLebesgueDecompositionMeasureTheory.SigmaFinite