theorem extracted_formal_statement_362.{u_1, w, u} {Ω : Type u} [inst : MeasurableSpace Ω] {Z : Type w} {n : ℕ}
  {ι : Type u_1} {f : ι → Z → ℝ} {μ : Measure Ω} [inst_1 : IsProbabilityMeasure μ] {X : Ω → Z} [inst_2 : Nonempty ι]
  [inst_3 : Countable ι] (hf : ∀ (i : ι), Measurable (f i ∘ X)) {b : ℝ} (hf' : ∀ (i : ι) (z : Z), |f i z| ≤ b)
  (i : Signs n) (hi : i ∈ Finset.univ) (i_1 : ι) (k0 : ∀ (k : Fin n), Measurable fun b => ↑↑(i k) * f i_1 (X (b.2 k))) :
  Measurable fun x => ∑ k, ↑↑(i k) * f i_1 (X (x.2 k)) := sorry

State before:
case left.hf.hf.h.hf.hf.hg.hf
Ω : Type u
inst✝³ : MeasurableSpace Ω
Z : Type w
n : ℕ
ι : Type u_1
f : ι → Z → ℝ
μ : Measure Ω
inst✝² : IsProbabilityMeasure μ
X : Ω → Z
inst✝¹ : Nonempty ι
inst✝ : Countable ι
hf : ∀ (i : ι), Measurable (f i ∘ X)
b : ℝ
hf' : ∀ (i : ι) (z : Z), |f i z| ≤ b
i : Signs n
hi : i ∈ Finset.univ
i_1 : ι
k0 : ∀ (k : Fin n), Measurable fun b => ↑↑(i k) * f i_1 (X (b.2 k))
⊢ Measurable fun x => ∑ k, ↑↑(i k) * f i_1 (X (x.2 k))

Tactic: exact Finset.measurable_sum Finset.univ fun i a ↦ k0 i

State after:

Relevant lemmas:
Finset.measurable_sum : ∀ {M : Type u_2} {ι : Type u_3} {α : Type u_4} [inst : AddCommMonoid M]
  [inst_4 : MeasurableSpace M] [inst_5 : 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