∀ {α : Type u_1} {β : Type u_2} {mα : MeasurableSpace α} {mβ : MeasurableSpace β} {f : α → β → ENNReal}
  (κ : ProbabilityTheory.Kernel α β) [inst : ProbabilityTheory.IsFiniteKernel κ],
  (∀ (a : α) (b : β), f a b ≠ ⊤) → ProbabilityTheory.IsSFiniteKernel (κ.withDensity f)