theorem extracted_formal_statement_54.{u_1} {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) :
  let e := fun t ω => rexp (t * X ω) * X ω;
  (∀ᶠ (x : ℝ) in nhds t, AEStronglyMeasurable (e x) μ) → ∀ (x : ℝ), AEStronglyMeasurable (e x) μ := sorry

State before:
case hF_meas
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
⊢ ∀ᶠ (x : ℝ) in nhds t, AEStronglyMeasurable (e x) μ

Tactic: apply Filter.Eventually.of_forall

State after:
[case hF_meas.hp
 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
 ⊢ ∀ (x : ℝ), AEStronglyMeasurable (e x) μ]

Relevant lemmas:
Filter.Eventually.of_forall : ∀ {α : Type u} {p : α → Prop} {f : Filter α}, (∀ (x : α), p x) → ∀ᶠ (x : α) in f, p x