∀ {Ω : Type u_1} {ι : Type u_2} {_mΩ : MeasurableSpace Ω} {μ : MeasureTheory.Measure Ω} {β : ι → Type u_10}
  {m : (i : ι) → MeasurableSpace (β i)} {f : (i : ι) → Ω → β i},
  ProbabilityTheory.iIndepFun f μ →
    (∀ (i : ι), Measurable (f i)) →
      ∀ (i j k : ι), i ≠ k → j ≠ k → ProbabilityTheory.IndepFun (fun a => (f i a, f j a)) (f k) μ