∀ {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} (S T : Finset ι),
  Disjoint S T →
    ProbabilityTheory.iIndepFun f μ →
      (∀ (i : ι), Measurable (f i)) → ProbabilityTheory.IndepFun (fun a i => f (↑i) a) (fun a i => f (↑i) a) μ