∀ {X : Type u_1} {E : Type u_3} {mX : MeasurableSpace X} {ι : Type u_5} [Countable ι] {μ : MeasureTheory.Measure X}
  [inst : NormedAddCommGroup E] {f : X → E} {s : ι → Set X},
  (∀ (i : ι), MeasureTheory.IntegrableOn f (s i) μ) →
    (Summable fun i => ∫ (x : X) in s i, ‖f x‖ ∂μ) → MeasureTheory.IntegrableOn f (Set.iUnion s) μ