∀ {α : Type u_1} {Ω : Type u_2} {β : Type u_4} {β' : Type u_5} {mα : MeasurableSpace α} {mΩ : MeasurableSpace Ω}
  {κ : ProbabilityTheory.Kernel α Ω} {μ : MeasureTheory.Measure α} {f : Ω → β} {g : Ω → β'} {mβ : MeasurableSpace β}
  {mβ' : MeasurableSpace β'} {f' : Ω → β} {g' : Ω → β'},
  ProbabilityTheory.Kernel.IndepFun f g κ μ →
    (∀ᵐ (a : α) ∂μ, f =ᵐ[κ a] f') → (∀ᵐ (a : α) ∂μ, g =ᵐ[κ a] g') → ProbabilityTheory.Kernel.IndepFun f' g' κ μ