theorem extracted_formal_statement_115.{u_1, w, u} {Ω : Type u} [inst : MeasurableSpace Ω] {Z : Type w} {ι : Type u_1}
  [inst_1 : AddCommMonoid Z] [inst_2 : MeasurableSpace Z] [inst_3 : MeasurableAdd₂ Z] {X : Ω → Z} (hX : Measurable X)
  (s : Finset ι) (h_original_goal : Measurable fun ω => ∑ k ∈ s, X (ω k)) (i : ι) :
  i ∈ s → Measurable fun a => X (a i) := sorry

State before:
Ω : Type u
inst✝³ : MeasurableSpace Ω
Z : Type w
ι : Type u_1
inst✝² : AddCommMonoid Z
inst✝¹ : MeasurableSpace Z
inst✝ : MeasurableAdd₂ Z
X : Ω → Z
hX : Measurable X
s : Finset ι
⊢ Measurable fun ω => ∑ k ∈ s, X (ω k)

Tactic: apply s.measurable_sum

State after:
[Ω : Type u
 inst✝³ : MeasurableSpace Ω
 Z : Type w
 ι : Type u_1
 inst✝² : AddCommMonoid Z
 inst✝¹ : MeasurableSpace Z
 inst✝ : MeasurableAdd₂ Z
 X : Ω → Z
 hX : Measurable X
 s : Finset ι
 ⊢ ∀ i ∈ s, Measurable fun a => X (a i)]

Relevant lemmas: