∀ {Ω : Type u_1} {mΩ : MeasurableSpace Ω} {μ : MeasureTheory.Measure Ω} {ι : Type u_2} {X : ι → Ω → ℝ},
  ProbabilityTheory.iIndepFun X μ →
    ∀ {c : ι → NNReal} {s : Finset ι},
      (∀ i ∈ s, ProbabilityTheory.HasSubgaussianMGF (X i) (c i) μ) →
        ProbabilityTheory.HasSubgaussianMGF (fun ω => ∑ i ∈ s, X i ω) (∑ i ∈ s, c i) μ