theorem extracted_formal_statement_50.{w, v, u} {Z : Type w} {ι : Type v} {f : ι → Z → ℝ} {Ω : Type u}
  [inst : MeasurableSpace Ω] {X : Ω → Z} [inst_1 : Countable ι] (h𝓕 : ∀ (I : ι), Measurable (f I ∘ X)) {n : ℕ} {I : ι}
  (h_original_goal : Measurable fun ω => ∑ i, (f I (X (ω i).1) - f I (X (ω i).2))) (i : Fin n) :
  i ∈ Finset.univ → Measurable fun a => f I (X (a i).1) - f I (X (a i).2) := sorry

State before:
Z : Type w
ι : Type v
f : ι → Z → ℝ
Ω : Type u
inst✝¹ : MeasurableSpace Ω
X : Ω → Z
inst✝ : Countable ι
h𝓕 : ∀ (I : ι), Measurable (f I ∘ X)
n : ℕ
I : ι
⊢ Measurable fun ω => ∑ i, (f I (X (ω i).1) - f I (X (ω i).2))

Tactic: apply Finset.measurable_sum Finset.univ

State after:
[Z : Type w
 ι : Type v
 f : ι → Z → ℝ
 Ω : Type u
 inst✝¹ : MeasurableSpace Ω
 X : Ω → Z
 inst✝ : Countable ι
 h𝓕 : ∀ (I : ι), Measurable (f I ∘ X)
 n : ℕ
 I : ι
 ⊢ ∀ i ∈ Finset.univ, Measurable fun a => f I (X (a i).1) - f I (X (a i).2)]

Relevant lemmas:
Finset.measurable_sum : ∀ {M : Type u_2} {ι : Type u_3} {α : Type u_4} [inst : AddCommMonoid M]
  [inst_2 : MeasurableSpace M] [inst_3 : MeasurableAdd₂ M] {m : MeasurableSpace α} {f : ι → α → M} (s : Finset ι),
  (∀ i ∈ s, Measurable (f i)) → Measurable fun a => ∑ i ∈ s, f i a