English
The toMeasurableSpace construction yields a MeasurableSpace α along with the cliqued properties, given a closure of intersections in the Dynkin system.
Русский
Конструкция toMeasurableSpace образует σ‑алгебру на α совместно с необходимыми свойствами, если в Dynkin-системе есть замыкание по пересечениям.
LaTeX
$$$\text{toMeasurableSpace}: \text{MeasurableSpace α}$ with given properties$$
Lean4
/-- The least Dynkin system containing a collection of basic sets.
This inductive type gives the underlying collection of sets. -/
inductive GenerateHas (s : Set (Set α)) : Set α → Prop
| basic : ∀ t ∈ s, GenerateHas s t
| empty : GenerateHas s ∅
| compl : ∀ {a}, GenerateHas s a → GenerateHas s aᶜ
| iUnion : ∀ {f : ℕ → Set α}, Pairwise (Disjoint on f) → (∀ i, GenerateHas s (f i)) → GenerateHas s (⋃ i, f i)
