∀ {α : Type u_1} {β : Type u_2} {mα : MeasurableSpace α} {mβ : MeasurableSpace β} {κ : ProbabilityTheory.Kernel α β}
  {t : Set (α × β)},
  MeasurableSet t → (∀ (a : α), MeasureTheory.IsFiniteMeasure (κ a)) → Measurable fun a => (κ a) (Prod.mk a ⁻¹' t)