∀ {Ω : Type u_1} {Ω' : Type u_2} {mΩ : MeasurableSpace Ω} {mΩ' : MeasurableSpace Ω'} {ν : MeasureTheory.Measure Ω'}
  {κ : ProbabilityTheory.Kernel Ω' Ω} {X : Ω → ℝ} {c : NNReal},
  ProbabilityTheory.Kernel.HasSubgaussianMGF X c κ ν →
    ∀ (t : ℝ), ∀ᵐ (ω' : Ω') ∂ν, MeasureTheory.Integrable (fun y => Real.exp (t * X y)) (κ ω')