theorem extracted_formal_statement_321.{u_1, w, u} {Ω : Type u} [inst : MeasurableSpace Ω] {Z : Type w} {n : ℕ}
  {ι : Type u_1} {f : ι → Z → ℝ} {X : Ω → Z} [inst_3 : Countable ι] (hf : ∀ (i : ι), Measurable (f i ∘ X)) (i : ι)
  (h_original_goal : Measurable fun b => |∑ k, (f i (X (b.1 k)) - f i (X (b.2 k)))|) :
  Measurable fun x => ∑ k, (f i (X (x.1 k)) - f i (X (x.2 k))) := sorry

State before:
case hf
Ω : Type u
inst✝ : MeasurableSpace Ω
Z : Type w
n : ℕ
ι : Type u_1
f : ι → Z → ℝ
X : Ω → Z
inst_3 : Countable ι
hf : ∀ (i : ι), Measurable (f i ∘ X)
i : ι
⊢ Measurable fun b => |∑ k, (f i (X (b.1 k)) - f i (X (b.2 k)))|

Tactic: apply Measurable.abs

State after:
[case hf.hf
 Ω : Type u
 inst✝ : MeasurableSpace Ω
 Z : Type w
 n : ℕ
 ι : Type u_1
 f : ι → Z → ℝ
 X : Ω → Z
 inst_3 : Countable ι
 hf : ∀ (i : ι), Measurable (f i ∘ X)
 i : ι
 ⊢ Measurable fun x => ∑ k, (f i (X (x.1 k)) - f i (X (x.2 k)))]

Relevant lemmas:
Measurable.abs : ∀ {α : Type u_1} {β : Type u_2} [inst : Lattice α] [inst_1 : AddGroup α] [inst_2 : MeasurableSpace α]
  [inst_4 : MeasurableSpace β] {f : β → α} [inst_5 : MeasurableNeg α] [inst_6 : MeasurableSup₂ α],
  Measurable f → Measurable fun x => |f x|