Sigma-algebra/Definition

Note: This page is intended to allow transclusion of the definition (so one copy is used many times), for the definition of $\sigma$-algebra see sigma-algebra

Definition

Given a set $X$ a $\sigma$-algebra on $X$ is a family of subsets of $X$, $\mathcal{A}$, such that:

• $\forall A\in\mathcal{A}[A^C\in\mathcal{A}]$ - Stable under complements
• $\forall\{A_n\}_{n=1}^\infty\subseteq\mathcal{A}\left[\bigcup_{n=1}^\infty A_n\in\mathcal{A}\right]$ - Stable under countable union