Theorems · Theorem · measure theory

MeasureTheory.Measure.rnDeriv_withDensity_withDensity_rnDeriv_left

∀ {α : Type u_1} {m : MeasurableSpace α} {f : α → ENNReal} (μ ν : MeasureTheory.Measure α) [MeasureTheory.SigmaFinite μ]
  [MeasureTheory.SigmaFinite ν],
  (∀ᵐ (x : α) ∂μ, f x ≠ ⊤) → ((ν.withDensity (μ.rnDeriv ν)).withDensity f).rnDeriv ν =ᵐ[ν] (μ.withDensity f).rnDeriv ν

Auxiliary lemma for rnDeriv_withDensity_left.

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.SigmaFinite