\begin{definition}[Definition:Sigma-Ring/Definition 1]
A '''$\sigma$-ring''' is a ring of sets which is closed under countable unions.
That is, a ring of sets $\Sigma$ is a '''$\sigma$-ring''' {{iff}}:
:$\ds A_1, A_2, \ldots \in \Sigma \implies \bigcup_{n \mathop = 1}^\infty A_n \in \Sigma$
\end{definition}