∀ {α : Type u_1} {β : Type u_2} {γ : Type u_3} {mα : MeasurableSpace α} {mβ : MeasurableSpace β}
  {mγ : MeasurableSpace γ} (κ : ProbabilityTheory.Kernel α β) [ProbabilityTheory.IsSFiniteKernel κ]
  (η : ProbabilityTheory.Kernel (α × β) γ) [ProbabilityTheory.IsSFiniteKernel η] (a : α) {f : β × γ → ENNReal},
  Measurable f →
    ∀ {s : Set β},
      MeasurableSet s →
        ∫⁻ (z : β × γ) in s ×ˢ Set.univ, f z ∂(κ.compProd η) a = ∫⁻ (x : β) in s, ∫⁻ (y : γ), f (x, y) ∂η (a, x) ∂κ a