∀ {Ω : Type u_1} {m : MeasurableSpace Ω} {μ : MeasureTheory.Measure Ω} [MeasureTheory.IsFiniteMeasure μ] {X : Ω → ℝ}
  (t b : ℝ),
  0 ≤ t → AEMeasurable X μ → (∀ᵐ (ω : Ω) ∂μ, X ω ≤ b) → MeasureTheory.Integrable (fun ω => Real.exp (t * X ω)) μ