Theorems · Theorem · measure theory

MeasureTheory.LocallyIntegrable.continuous_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] [inst_7 : Module 𝕜 E] [NormSMulClass 𝕜 E] [SecondCountableTopologyEither X 𝕜] {f : X → E}
  {g : X → 𝕜},
  Continuous g → MeasureTheory.LocallyIntegrable f μ → MeasureTheory.LocallyIntegrable (fun x => g x • f x) μ

Defined in

Mathlib.MeasureTheory.Function.LocallyIntegrable

Cited by

0 results in Mathlib

Foundations

Depth 221 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

MeasurableSpaceTopologicalSpaceNormedAddCommGroupOpensMeasurableSpaceLocallyCompactSpaceT2SpaceNormedRingModuleNormSMulClassSecondCountableTopologyEither