theorem extracted_formal_statement_85 : Measurable abs := sorry

State before:
Ω : Type u_1
m : MeasurableSpace Ω
μ : Measure Ω
inst✝ : IsFiniteMeasure μ
t a b : ℝ
X : Ω → ℝ
hX : AEMeasurable X μ
h : ∀ᵐ (ω : Ω) ∂μ, X ω ∈ Set.Icc a b
c : ℝ := ‖a‖ ⊔ ‖b‖
e : ℝ → Ω → ℝ := fun t ω => rexp (t * X ω) * X ω
e' : ℝ → Ω → ℝ := fun t ω => rexp (t * X ω) * X ω ^ 2
⊢ AEMeasurable (fun ω => |X ω|) μ

Tactic: apply Measurable.comp_aemeasurable' _ hX

State after:
[Ω : Type u_1
 m : MeasurableSpace Ω
 μ : Measure Ω
 inst✝ : IsFiniteMeasure μ
 t a b : ℝ
 X : Ω → ℝ
 hX : AEMeasurable X μ
 h : ∀ᵐ (ω : Ω) ∂μ, X ω ∈ Set.Icc a b
 c : ℝ := ‖a‖ ⊔ ‖b‖
 e : ℝ → Ω → ℝ := fun t ω => rexp (t * X ω) * X ω
 e' : ℝ → Ω → ℝ := fun t ω => rexp (t * X ω) * X ω ^ 2
 ⊢ Measurable abs]

Relevant lemmas:
Measurable.comp_aemeasurable' : ∀ {α : Type u_1} {β : Type u_2} {δ : Type u_4} {m : MeasurableSpace α}
  [inst : MeasurableSpace β] {μ : Measure α} [inst_1 : MeasurableSpace δ] {f : α → δ} {g : δ → β},
  Measurable g → AEMeasurable f μ → AEMeasurable (fun x => g (f x)) μ