Theorems · Theorem · measure theory

aemeasurable_withDensity_iff

∀ {α : Type u_1} {m : MeasurableSpace α} {μ : MeasureTheory.Measure α} {E : Type u_2} [inst : NormedAddCommGroup E]
  [inst_1 : NormedSpace ℝ E] [SecondCountableTopology E] [inst_3 : MeasurableSpace E] [BorelSpace E] {f : α → NNReal},
  Measurable f → ∀ {g : α → E}, AEMeasurable g (μ.withDensity fun x => ↑(f x)) ↔ AEMeasurable (fun x => ↑(f x) • g x) μ

Defined in

Mathlib.MeasureTheory.Integral.LebesgueNormedSpace

Cited by

0 results in Mathlib

Foundations

Depth 208 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupNormedSpaceSecondCountableTopologyMeasurableSpaceBorelSpace