Sigma-Ring contains Limit Superior of Sequence of Sets

Theorem
Let $\RR$ be a $\sigma$-ring.

Let $\sequence {A_n}_{n \mathop \in \N} \in \RR$ be a sequence of sets in $\RR$.

Then:
 * $\ds \limsup_{n \mathop \to \infty} A_n \in \RR$