Definition 19.1.3 ($\sigma$-Algebra).label Let $X$ be a set and $\cm \subset 2^{X}$, then $\cm$ is a $\sigma$-algebra if:

1. (A1)

   $\emptyset, X \in \cm$.

2. (A2)

   For any $A \in \cm$, $A^{c} \in \cm$.

3. (A3’)

   For any $\seq{A_n}\in \cm$, $\bigcup_{n \in \nat^+}A_{n} \in \cm$.