Theorems · Theorem · measure theory

MeasureTheory.integral_rnDeriv_smul

∀ {α : Type u_3} {m : MeasurableSpace α} {μ ν : MeasureTheory.Measure α} {E : Type u_4} [inst : NormedAddCommGroup E]
  [inst_1 : NormedSpace ℝ E] [μ.HaveLebesgueDecomposition ν] [MeasureTheory.SigmaFinite μ] {f : α → E},
  μ.AbsolutelyContinuous ν → ∫ (x : α), (μ.rnDeriv ν x).toReal • f x ∂ν = ∫ (x : α), f x ∂μ

Defined in

Mathlib.MeasureTheory.Measure.Decomposition.RadonNikodym

Cited by

5 results in Mathlib

Foundations

Depth 265 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupNormedSpaceMeasureTheory.Measure.HaveLebesgueDecompositionMeasureTheory.SigmaFinite