theorem extracted_formal_statement_10.{u_1} {Ω : Type u_1} {m : MeasurableSpace Ω} {μ : Measure Ω}
  [inst : IsFiniteMeasure μ] {X : Ω → ℝ} {t a b : ℝ} (hX : AEMeasurable X μ) (h : ∀ᵐ (ω : Ω) ∂μ, X ω ∈ Set.Icc a b)
  (ht : 0 < t) : Integrable (fun ω => rexp (t * X ω)) μ := sorry

State before:
case inr.inr
Ω : Type u_1
m : MeasurableSpace Ω
μ : Measure Ω
inst✝ : IsFiniteMeasure μ
X : Ω → ℝ
t a b : ℝ
hX : AEMeasurable X μ
h : ∀ᵐ (ω : Ω) ∂μ, X ω ∈ Set.Icc a b
ht : 0 < t
⊢ Integrable (fun ω => rexp (t * X ω)) μ

Tactic: exact integrable_expt t b ht hX (h.mono fun ω h ↦ h.2)

State after:

Relevant lemmas: