Sigma-ring

A Sigma-ring or

$$\sigma$$ -ring, is closely related to rings of sets, and just like algebras of sets are related to rings of sets, so is $$\sigma$$ -ring to $$\sigma$$ -algebra

Definition

A non-empty class of sets $S$ is a $\sigma$-ring if:

• for $A\in S$ and $B\in S$ then $A-B\in S$
• If $$\{A_n\}_{n=1}^\infty\subset S$$ then $$\cup^\infty_{n=1}A_n\in S$$

That is to say it is closed under subtraction and countable union