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:
 * $$A_1, A_2, \ldots \in \mathcal R \implies \bigcup_{n=1}^\infty A_n \in \mathcal R$$