∀ {X : Type u_1} {E : Type u_3} {mX : MeasurableSpace X} {ι : Type u_5} [Countable ι] {μ : MeasureTheory.Measure X}
  [inst : NormedAddCommGroup E] [inst_1 : TopologicalSpace X] [BorelSpace X] [T2Space X]
  [MeasureTheory.IsLocallyFiniteMeasure μ] {f : C(X, E)} {s : ι → TopologicalSpace.Compacts X},
  (Summable fun i => ‖ContinuousMap.restrict (↑(s i)) f‖ * μ.real ↑(s i)) →
    MeasureTheory.IntegrableOn (⇑f) (⋃ i, ↑(s i)) μ