Let A 1 , A 2 , … be a collection of events, and let...

Let $A_1,A_2,\dots$ be a collection of events, and let $\mathcal{A}$ be the smallest $\sigma$-field of subsets of $\mathrm{\Omega }$ which contains all of them. If $A\in \mathcal{A}$, then there exists a sequence of events $\left\{C_n\right\}$ such that
$C_n\in {\mathcal{A}}_n\text{ and }\mathbb{P}\left(A\mathrm{△}{C}_n\right)\to 0\text{ as }n\to \mathrm{\infty }$
where ${\mathcal{A}}_n$ is the smallest $\sigma$-field which contains the finite collection $A_1,A_2,\dots ,A_n.$
However, I do not know how to choose the $C_n$ such that they turn up in $\sigma (A_1,..A_n)$?