Definition

countable/co-countable σ\sigma-field

the set {A⊂ℝ:A is countable}∪{A⊂ℝ:A∁ is countable} \{ A \subset \mathbb{R} : A \textrm{ is countable} \} \cup \{ A \subset \mathbb{R} : A^{\complement} \textrm{ is countable} \} , where Ω=ℝ\Omega = \mathbb{R}