A sigma-algebra (or $\sigma$-algebra) is a collection $\Sigma$ of subsets of a set $\Omega$ such that
- $\Omega \in \Sigma$ .
- Closed under complementation: If a set $A \in \Sigma$, then $X \setminus A \in \Sigma$.
- Closed under countable unions: If $A_1, A_2, A_3, \ldots$ are in $\Sigma$, then so is $A = A_1 \cup A_2 \cup A_3 \cup \ldots$.