Theorems · Theorem · measure theory

MeasureTheory.Measure.rnDeriv_withDensity_left

∀ {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) ∂μ, f x ≠ ⊤) → (μ.withDensity f).rnDeriv ν =ᵐ[ν] fun x => f x * μ.rnDeriv ν x

Defined in

Mathlib.MeasureTheory.Measure.Decomposition.RadonNikodym

Cited by

2 results in Mathlib

Foundations

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

Assumes

MeasureTheory.SigmaFiniteMeasureTheory.SigmaFinite