Intersection of Sigma-Algebras

Theorem
Let $X$ be a set.

Let $\left({\mathcal{A}_i}\right)_{i \in I}$ be a collection of $\sigma$-algebras on $X$.

Then $\displaystyle \bigcap_{i \in I} \mathcal{A}_i$ is also a $\sigma$-algebra on $X$.

Here, $\displaystyle \bigcap$ denotes set intersection.