∀ {α : Type u_1} {β : Type u_2} {mα : MeasurableSpace α} {mβ : MeasurableSpace β} {μ : MeasureTheory.Measure α}
  {κ η : ProbabilityTheory.Kernel α β} [MeasurableSpace.CountableOrCountablyGenerated α β]
  [MeasureTheory.IsFiniteMeasure μ] [ProbabilityTheory.IsFiniteKernel κ] [ProbabilityTheory.IsFiniteKernel η],
  μ.compProd κ = μ.compProd η → ⇑κ =ᵐ[μ] ⇑η