Theorems · Theorem · measure theory

MeasurableEmbedding.rnDeriv_map_aux

∀ {α : Type u_1} {β : Type u_2} {m : MeasurableSpace α} {μ ν : MeasureTheory.Measure α} {mβ : MeasurableSpace β}
  {f : α → β},
  MeasurableEmbedding f →
    μ.AbsolutelyContinuous ν →
      ∀ [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 216 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

MeasureTheory.SigmaFiniteMeasureTheory.SigmaFinite