\begin{definition}[Definition:Sigma-Algebra/Definition 2]
Let $X$ be a set.
A '''$\sigma$-algebra''' $\Sigma$ over $X$ is a system of subsets of $X$ with the following properties:
{{begin-axiom}}
{{axiom | n = \text {SA} 1'
        | lc= Unit:
        | m = X \in \Sigma
}}
{{axiom | n = \text {SA} 2'
        | lc= Closure under Complement:
        | q = \forall A \in \Sigma
        | m = \relcomp X A \in \Sigma
}}
{{axiom | n = \text {SA} 3'
        | lc= Closure under Countable Disjoint Unions:
        | q = \forall A_n \in \Sigma: n = 1, 2, \ldots
        | m = \bigsqcup_{n \mathop = 1}^\infty A_n \in \Sigma
}}
{{end-axiom}}
\end{definition}