Sigma-Ring contains Limit Superior of Sequence of Sets

Theorem
Let $\mathcal R$ be a $\sigma$-ring.

Let $\left \langle{A_n}\right \rangle_{n \mathop \in \N} \in \mathcal R$ be a sequence of sets in $\mathcal R$.

Then:
 * $\displaystyle \limsup_{n \to \infty} \ A_n \in \mathcal R$