∀ {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] {A K : Set X} {𝕜 : Type u_9} [inst_4 : NormedRing 𝕜]
  [inst_5 : Module 𝕜 E] [NormSMulClass 𝕜 E] [SecondCountableTopologyEither X E] {f : X → 𝕜},
  MeasureTheory.IntegrableOn f A μ →
    ∀ {g : X → E},
      ContinuousOn g K → MeasurableSet A → IsCompact K → A ⊆ K → MeasureTheory.IntegrableOn (fun x => f x • g x) A μ