∀ {α : Type u_1} {β : Type u_2} {ε : Type u_3} {mα : MeasurableSpace α} {f : α → ε} {μ : MeasureTheory.Measure α}
  [inst : TopologicalSpace ε] [inst_1 : ContinuousENorm ε] [TopologicalSpace.PseudoMetrizableSpace ε] {s : Finset β}
  {t : β → Set α}, MeasureTheory.IntegrableOn f (⋃ i ∈ s, t i) μ = ∀ i ∈ s, MeasureTheory.IntegrableOn f (t i) μ