∀ {α : Type u_1} {γ : Type u_2} {mα : MeasurableSpace α} {mγ : MeasurableSpace γ}
  [hαγ : MeasurableSpace.CountableOrCountablyGenerated α γ] (κ η : ProbabilityTheory.Kernel α γ)
  [inst : ProbabilityTheory.IsFiniteKernel κ] [inst_1 : ProbabilityTheory.IsFiniteKernel η],
  η.withDensity (κ.rnDeriv η) + κ.singularPart η = κ