Theorems · Theorem · measure theory

aemeasurable_smul_const

∀ {α : Type u_1} [inst : MeasurableSpace α] {𝕜 : Type u_2} [inst_1 : NontriviallyNormedField 𝕜] [CompleteSpace 𝕜]
  [inst_3 : MeasurableSpace 𝕜] [BorelSpace 𝕜] {E : Type u_3} [inst_5 : NormedAddCommGroup E] [inst_6 : NormedSpace 𝕜 E]
  [inst_7 : MeasurableSpace E] [BorelSpace E] {f : α → 𝕜} {μ : MeasureTheory.Measure α} {c : E},
  c ≠ 0 → (AEMeasurable (fun x => f x • c) μ ↔ AEMeasurable f μ)

Defined in

Mathlib.MeasureTheory.Constructions.BorelSpace.ContinuousLinearMap

Cited by

0 results in Mathlib

Foundations

Depth 183 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

MeasurableSpaceNontriviallyNormedFieldCompleteSpaceMeasurableSpaceBorelSpaceNormedAddCommGroupNormedSpaceMeasurableSpaceBorelSpace