measurableSet_lt_of_countable' — Mathlib

English

With Countable ι, measurability of {τ(ω) < i}.

Русский

С учётом счетного индекса, множество {τ(ω) < i} измеримо.

LaTeX

$$$\{ω : τ(ω) < i\}$ measurable in stopping-time sigma-algebra when ι is countable.$$

Lean4

protected theorem measurableSet_lt_of_countable' [Countable ι] (hτ : IsStoppingTime f τ) (i : ι) :
    MeasurableSet[hτ.measurableSpace] {ω | τ ω < i} :=
  hτ.measurableSet_lt_of_countable_range' (Set.to_countable _) i

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