Theorems · Theorem · measure theory

MeasureTheory.integral_toReal_rnDeriv_mul

∀ {α : Type u_3} {m : MeasurableSpace α} {μ ν : MeasureTheory.Measure α} [μ.HaveLebesgueDecomposition ν]
  [MeasureTheory.SigmaFinite μ],
  μ.AbsolutelyContinuous ν → ∀ {f : α → ℝ}, ∫ (x : α), (μ.rnDeriv ν x).toReal * f x ∂ν = ∫ (x : α), f x ∂μ

Defined in

Mathlib.MeasureTheory.Measure.Decomposition.RadonNikodym

Cited by

0 results in Mathlib

Foundations

Depth 266 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

MeasureTheory.Measure.HaveLebesgueDecompositionMeasureTheory.SigmaFinite