∀ {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 : β → E),
  ∫ (z : α × β), f z.2 ∂μ.prod ν = μ.real Set.univ • ∫ (y : β), f y ∂ν