theorem extracted_formal_statement_0.{u_2, u_1} {ι : Type u_1} {Ω : ι → Type u_2} [inst : Fintype ι]
  [inst_1 : (i : ι) → MeasurableSpace (Ω i)] {μ : (i : ι) → Measure (Ω i)}
  [inst_2 : ∀ (i : ι), IsProbabilityMeasure (μ i)] (k : ι)
  (h_original_goal : Measure.map (Function.eval k) (Measure.pi μ) = μ k) (s : Set (Ω k)) :
  MeasurableSet s → (Measure.map (Function.eval k) (Measure.pi μ)) s = (μ k) s := sorry

State before:
ι : Type u_1
Ω : ι → Type u_2
inst✝³ : Fintype ι
inst✝² : DecidableEq ι
inst✝¹ : (i : ι) → MeasurableSpace (Ω i)
μ : (i : ι) → Measure (Ω i)
inst✝ : ∀ (i : ι), IsProbabilityMeasure (μ i)
k : ι
⊢ Measure.map (Function.eval k) (Measure.pi μ) = μ k

Tactic: apply Measure.ext_iff.mpr

State after:
[ι : Type u_1
 Ω : ι → Type u_2
 inst✝³ : Fintype ι
 inst✝² : DecidableEq ι
 inst✝¹ : (i : ι) → MeasurableSpace (Ω i)
 μ : (i : ι) → Measure (Ω i)
 inst✝ : ∀ (i : ι), IsProbabilityMeasure (μ i)
 k : ι
 ⊢ ∀ (s : Set (Ω k)), MeasurableSet s → (Measure.map (Function.eval k) (Measure.pi μ)) s = (μ k) s]

Relevant lemmas: