Theorems · Theorem · measure theory

MeasureTheory.LocallyIntegrableOn.continuousOn_mul

∀ {X : Type u_1} {R : Type u_8} [inst : MeasurableSpace X] [inst_1 : TopologicalSpace X] {μ : MeasureTheory.Measure X}
  [OpensMeasurableSpace X] [LocallyCompactSpace X] [T2Space X] [inst_5 : NormedRing R]
  [SecondCountableTopologyEither X R] {f g : X → R} {s : Set X},
  MeasureTheory.LocallyIntegrableOn f s μ →
    ContinuousOn g s → IsLocallyClosed 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 221 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

MeasurableSpaceTopologicalSpaceOpensMeasurableSpaceLocallyCompactSpaceT2SpaceNormedRingSecondCountableTopologyEither