∀ {α : Type u_1} {β : Type u_2} {mα : MeasurableSpace α} {mβ : MeasurableSpace β} {κ η : ProbabilityTheory.Kernel α β},
  (∀ (a : α) (f : β → ENNReal), Measurable f → ∫⁻ (b : β), f b ∂κ a = ∫⁻ (b : β), f b ∂η a) → κ = η