-- File: FoML/FoML/Bennett.lean
Theorem statement:
theorem extracted_formal_statement_36.{u_1} {Ω : Type u_1} [inst : MeasurableSpace Ω] (μ : Measure Ω)
  [inst_1 : IsProbabilityMeasure μ] {n : ℕ} {X : Fin n → Ω → ℝ} (hXm : ∀ (i : Fin n), Measurable (X i))
  (hX_bdd : ∀ (i : Fin n), ∀ᵐ (ω : Ω) ∂μ, |X i ω| ≤ 1) (τ : ℝ) (hlam : τ ≥ 0) (i : Fin n)
  (hbdd : ∀ᵐ (ω : Ω) ∂μ, rexp (τ * X i ω) ∈ Icc (rexp (-τ)) (rexp τ))
  (h_bound : ∀ᵐ (ω : Ω) ∂μ, ‖rexp (τ * X i ω)‖ ≤ rexp τ) : HasFiniteIntegral (fun ω => rexp (τ * X i ω)) μ := sorry

Tactic state before:
case right
Ω : Type u_1
inst : MeasurableSpace Ω
μ : Measure Ω
inst_1 : IsProbabilityMeasure μ
n : ℕ
X : Fin n → Ω → ℝ
hXm : ∀ (i : Fin n), Measurable (X i)
hX_bdd : ∀ (i : Fin n), ∀ᵐ (ω : Ω) ∂μ, |X i ω| ≤ 1
τ : ℝ
hlam : τ ≥ 0
i : Fin n
hbdd : ∀ᵐ (ω : Ω) ∂μ, rexp (τ * X i ω) ∈ Icc (rexp (-τ)) (rexp τ)
h_bound : ∀ᵐ (ω : Ω) ∂μ, ‖rexp (τ * X i ω)‖ ≤ rexp τ
⊢ HasFiniteIntegral (fun ω => rexp (τ * X i ω)) μ

Tactic: exact hasFiniteIntegral_of_bounded h_bound

Tactic state after:

Premises used:
MeasureTheory.hasFiniteIntegral_of_bounded : ∀ {α : Type u_1} {β : Type u_2} {m : MeasurableSpace α} {μ : Measure α}
  [inst : NormedAddCommGroup β] [inst_2 : IsFiniteMeasure μ] {f : α → β} {C : ℝ},
  (∀ᵐ (a : α) ∂μ, ‖f a‖ ≤ C) → HasFiniteIntegral f μ