∀ {ι : Type u_1} {κ : ι → Type u_4} {𝓧 : (i : ι) → κ i → Type u_5} {m𝓧 : (i : ι) → (j : κ i) → MeasurableSpace (𝓧 i j)}
  {Ω : (i : ι) → κ i → Type u_6} {mΩ : (i : ι) → (j : κ i) → MeasurableSpace (Ω i j)}
  {X : (i : ι) → (j : κ i) → Ω i j → 𝓧 i j} (μ : (i : ι) → (j : κ i) → MeasureTheory.Measure (Ω i j))
  [∀ (i : ι) (j : κ i), MeasureTheory.IsProbabilityMeasure (μ i j)],
  (∀ (i : ι) (j : κ i), Measurable (X i j)) →
    ProbabilityTheory.iIndepFun (fun p ω => X p.fst p.snd (ω p.fst p.snd))
      (MeasureTheory.Measure.infinitePi fun i => MeasureTheory.Measure.infinitePi (μ i))