English
Define countableFiltration using countablePartition α n: F_n = generateFrom(countablePartition α n). This yields a filtration on m with F_n increasing in n.
Русский
Определим countableFiltration через countablePartition α n: F_n = generateFrom(countablePartition α n). Это образует филтрацию над m, при этом F_n возрастает с n.
LaTeX
$$$$ \text{countableFiltration}(\alpha) : \Filtration \mathbb{N} \, m \quad \text{with } \mathcal F_n = \operatorname{generateFrom}(\operatorname{countablePartition} \alpha n) $$$$
Lean4
/-- A filtration built from the measurable spaces generated by `countablePartition α n` for
all `n : ℕ`. -/
def countableFiltration (α : Type*) [m : MeasurableSpace α] [CountablyGenerated α] : Filtration ℕ m
where
seq n := generateFrom (countablePartition α n)
mono' := monotone_nat_of_le_succ (generateFrom_countablePartition_le_succ _)
le' := generateFrom_countablePartition_le α
