Theorems · Theorem · measure theory

MeasureTheory.Measure.rnDeriv_withDensity_left_of_absolutelyContinuous

∀ {α : Type u_1} {m : MeasurableSpace α} {μ : MeasureTheory.Measure α} {f : α → ENNReal} {ν : MeasureTheory.Measure α}
  [MeasureTheory.SigmaFinite μ] [MeasureTheory.SigmaFinite ν],
  μ.AbsolutelyContinuous ν → AEMeasurable f ν → (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 215 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

MeasureTheory.SigmaFiniteMeasureTheory.SigmaFinite