Theorems · Theorem · measure theory

MeasureTheory.Measure.setIntegral_toReal_rnDeriv_eq_withDensity

∀ {α : Type u_1} {m : MeasurableSpace α} {μ ν : MeasureTheory.Measure α} [MeasureTheory.SigmaFinite μ]
  [MeasureTheory.SFinite ν] (s : Set α),
  ∫ (x : α) in s, (μ.rnDeriv ν x).toReal ∂ν = (ν.withDensity (μ.rnDeriv ν)).real s

Defined in

Mathlib.MeasureTheory.Measure.Decomposition.RadonNikodym

Cited by

2 results in Mathlib

Foundations

Depth 255 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

MeasureTheory.SigmaFiniteMeasureTheory.SFinite