∀ {α : Type u_1} {Ω : Type u_2} {ι : Type u_3} {mα : MeasurableSpace α} {mΩ : MeasurableSpace Ω}
  {κ : ProbabilityTheory.Kernel α Ω} {μ : MeasureTheory.Measure α} {β : ι → Type u_8} {γ : ι → Type u_9}
  {mβ : (i : ι) → MeasurableSpace (β i)} {mγ : (i : ι) → MeasurableSpace (γ i)} {f : (i : ι) → Ω → β i},
  ProbabilityTheory.Kernel.iIndepFun f κ μ →
    ∀ (g : (i : ι) → β i → γ i),
      (∀ (i : ι), Measurable (g i)) → ProbabilityTheory.Kernel.iIndepFun (fun i => g i ∘ f i) κ μ