Theorems · Theorem · measure theory

MeasureTheory.Measure.rnDeriv_withDensity_right

∀ {α : Type u_1} {m : MeasurableSpace α} {f : α → ENNReal} (μ ν : MeasureTheory.Measure α) [MeasureTheory.SigmaFinite μ]
  [MeasureTheory.SigmaFinite ν],
  AEMeasurable f ν →
    (∀ᵐ (x : α) ∂ν, f x ≠ 0) →
      (∀ᵐ (x : α) ∂ν, f x ≠ ⊤) → μ.rnDeriv (ν.withDensity f) =ᵐ[ν] fun x => (f x)⁻¹ * μ.rnDeriv ν x

Defined in

Mathlib.MeasureTheory.Measure.Decomposition.RadonNikodym

Cited by

1 results in Mathlib

Foundations

Depth 218 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

MeasureTheory.SigmaFiniteMeasureTheory.SigmaFinite