∀ {Ω : Type u_1} {m : MeasurableSpace Ω} {X : Ω → ℝ} {μ : MeasureTheory.Measure Ω} {Ω' : Type u_3}
  {mΩ' : MeasurableSpace Ω'} {μ' : MeasureTheory.Measure Ω'} {Y : Ω' → ℝ},
  ProbabilityTheory.IdentDistrib X Y μ μ' → ProbabilityTheory.mgf X μ = ProbabilityTheory.mgf Y μ'