Let \(\left\{A_{n}ight\}_{n=1}^{\infty}\) be a sequence of events from a \(\sigma\)-field \(\mathcal{F}\) of subsets of a sample space \(\Omega\). Prove that if \(A_{n+1} \subset A_{n}\) for all \(n \in \mathbb{N}\) then the sequence has limit

\[\lim _{n ightarrow \infty} A_{n}=\bigcap_{n=1}^{\infty} A_{n}\]