∀ {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] {K : Set X} {f : X → E}
  [MeasureTheory.IsLocallyFiniteMeasure μ] [SecondCountableTopologyEither X E],
  ContinuousOn f K → MeasurableSet K → MeasureTheory.LocallyIntegrableOn f K μ