∀ {Ω : Type u_1} {ι : Type u_2} {m : MeasurableSpace Ω} {μ : MeasureTheory.Measure Ω} {X : ι → Ω → ℝ} {s : Finset ι}
  {j : ι},
  (∀ (i : ι), AEMeasurable (X i) μ) →
    ProbabilityTheory.iIndepFun X μ →
      (∀ i ∈ s, ∀ j ∈ s, ProbabilityTheory.IdentDistrib (X i) (X j) μ μ) →
        j ∈ s → ∀ (t : ℝ), ProbabilityTheory.mgf (∑ i ∈ s, X i) μ t = ProbabilityTheory.mgf (X j) μ t ^ s.card