Theorems · Theorem · measure theory

MeasureTheory.LocallyIntegrableOn.continuousOn_smul

∀ {X : Type u_1} {E : Type u_6} [inst : MeasurableSpace X] [inst_1 : TopologicalSpace X] [inst_2 : NormedAddCommGroup E]
  {μ : MeasureTheory.Measure X} [OpensMeasurableSpace X] [LocallyCompactSpace X] [T2Space X] {𝕜 : Type u_9}
  [inst_6 : NormedRing 𝕜] [SecondCountableTopologyEither X 𝕜] [inst_8 : Module 𝕜 E] [IsBoundedSMul 𝕜 E] {f : X → E}
  {g : X → 𝕜} {s : Set X},
  IsLocallyClosed s →
    MeasureTheory.LocallyIntegrableOn f s μ →
      ContinuousOn g s → MeasureTheory.LocallyIntegrableOn (fun x => g x • f x) s μ

Defined in

Mathlib.MeasureTheory.Function.LocallyIntegrable

Cited by

2 results in Mathlib

Foundations

Depth 220 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

MeasurableSpaceTopologicalSpaceNormedAddCommGroupOpensMeasurableSpaceLocallyCompactSpaceT2SpaceNormedRingSecondCountableTopologyEitherModuleIsBoundedSMul