sigma–ring of sets

A $\sigma$-ring of sets is a nonempty collection $𝒮$ of sets such that

• if $A\in 𝒮$ and $B\in 𝒮$ then $A-B\in 𝒮$ and

• if $A_i\in 𝒮$ for $i=1,2\mathrm{\dots },$ then ${\cup }_{i=1}^{\mathrm{\infty }}{A}_i\in 𝒮$

A $\sigma$-ring is also closed under countable intersections since

$${\cap }_{i=1}^{\mathrm{\infty }}{A}_i=A-{\cup }_{i=1}^{\mathrm{\infty }}(A-A_i)$$

where $A={\cup }_{i=1}^{\mathrm{\infty }}{A}_i$.

$\sigma$-rings are used in measure theory.