∀ {α : Type u_1} {β : Type u_2} {E : Type u_3} [inst : MeasurableSpace α] [inst_1 : MeasurableSpace β]
  {μ : MeasureTheory.Measure α} {ν : MeasureTheory.Measure β} [inst_2 : NormedAddCommGroup E] [MeasureTheory.SFinite ν]
  [inst_4 : NormedSpace ℝ E] [MeasureTheory.SFinite μ] ⦃f g : α × β → E⦄,
  MeasureTheory.Integrable f (μ.prod ν) →
    MeasureTheory.Integrable g (μ.prod ν) →
      ∫ (x : α), ∫ (y : β), (f - g) (x, y) ∂ν ∂μ =
        ∫ (x : α), ∫ (y : β), f (x, y) ∂ν ∂μ - ∫ (x : α), ∫ (y : β), g (x, y) ∂ν ∂μ