Definition 13.1.3 ($\sigma$-Algebra). Let $X$ be a set and $\cm \subset 2^{X}$, then $\cm$ is a $\sigma$-algebra if:
$\emptyset, X \in \cm$.
For any $A \in \cm$, $A^{c} \in \cm$.
For any $\seq{A_n}\in \cm$, $\bigcup_{n \in \nat^+}A_{n} \in \cm$.
Definition 13.1.3 ($\sigma$-Algebra). Let $X$ be a set and $\cm \subset 2^{X}$, then $\cm$ is a $\sigma$-algebra if:
$\emptyset, X \in \cm$.
For any $A \in \cm$, $A^{c} \in \cm$.
For any $\seq{A_n}\in \cm$, $\bigcup_{n \in \nat^+}A_{n} \in \cm$.