Theorems · Theorem · measure theory

MeasureTheory.IntegrableOn.mul_continuousOn_of_subset

∀ {X : Type u_1} {R : Type u_8} [inst : MeasurableSpace X] [inst_1 : TopologicalSpace X] {μ : MeasureTheory.Measure X}
  [OpensMeasurableSpace X] {A K : Set X} [inst_3 : NormedRing R] [SecondCountableTopologyEither X R] {g g' : X → R},
  MeasureTheory.IntegrableOn g A μ →
    ContinuousOn g' K → MeasurableSet A → IsCompact K → A ⊆ K → MeasureTheory.IntegrableOn (fun x => g x * g' x) A μ

Defined in

Mathlib.MeasureTheory.Function.LocallyIntegrable

Cited by

2 results in Mathlib

Foundations

Depth 219 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

MeasurableSpaceTopologicalSpaceOpensMeasurableSpaceNormedRingSecondCountableTopologyEither