Definition:Sigma-Ring

Definition
A sigma-ring (which can conveniently be written $\sigma$-ring) is a ring of sets which is closed under countable unions.

That is, a ring of sets $\mathcal R$ is a sigma-ring iff:
 * $\displaystyle A_1, A_2, \ldots \in \mathcal R \implies \bigcup_{n=1}^\infty A_n \in \mathcal R$