Theorems · Theorem · measure theory

MeasurableEmbedding.rnDeriv_map

∀ {α : Type u_1} {β : Type u_2} {m : MeasurableSpace α} {mβ : MeasurableSpace β} {f : α → β},
  MeasurableEmbedding f →
    ∀ (μ ν : MeasureTheory.Measure α) [MeasureTheory.SigmaFinite μ] [MeasureTheory.SigmaFinite ν],
      (fun x => (MeasureTheory.Measure.map f μ).rnDeriv (MeasureTheory.Measure.map f ν) (f x)) =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.SigmaFinite