∀ {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} {π : ι → Set (Set Ω)} {s : ι → Set Ω}
  [inst : Fintype ι],
  ProbabilityTheory.Kernel.iIndepSets π κ μ →
    (∀ (i : ι), s i ∈ π i) → ∀ᵐ (a : α) ∂μ, (κ a) (⋂ i, s i) = ∏ i, (κ a) (s i)