theorem extracted_formal_statement_179.{u_1, w, u} {Ω : Type u} [inst : MeasurableSpace Ω] {Z : Type w} {n : ℕ}
  {ι : Type u_1} {f : ι → Z → ℝ} [inst_1 : Countable ι] {X : Ω → Z} (hf : ∀ (i : ι), Measurable (f i ∘ X))
  (h_original_goal : Measurable fun a => ∑ σ, ⨆ i, |∑ k, ↑↑(σ k) * f i (X (a k).1)|) (i : Signs n) :
  i ∈ Finset.univ → Measurable fun a => ⨆ i_1, |∑ k, ↑↑(i k) * f i_1 (X (a k).1)| := sorry

State before:
Ω : Type u
inst✝¹ : MeasurableSpace Ω
Z : Type w
n : ℕ
ι : Type u_1
f : ι → Z → ℝ
inst✝ : Countable ι
X : Ω → Z
hf : ∀ (i : ι), Measurable (f i ∘ X)
⊢ Measurable fun a => ∑ σ, ⨆ i, |∑ k, ↑↑(σ k) * f i (X (a k).1)|

Tactic: apply Finset.univ.measurable_sum

State after:
[Ω : Type u
 inst✝¹ : MeasurableSpace Ω
 Z : Type w
 n : ℕ
 ι : Type u_1
 f : ι → Z → ℝ
 inst✝ : Countable ι
 X : Ω → Z
 hf : ∀ (i : ι), Measurable (f i ∘ X)
 ⊢ ∀ i ∈ Finset.univ, Measurable fun a => ⨆ i_1, |∑ k, ↑↑(i k) * f i_1 (X (a k).1)|]

Relevant lemmas: