Sigma-Algebra is Monotone Class

Theorem
Let $\Sigma$ be a $\sigma$-algebra on a set $X$.

Then $\Sigma$ is also a monotone class.

Proof
By definition, $\Sigma$, being a $\sigma$-algebra, is closed under countable unions.

From Sigma-Algebra Closed under Countable Intersection, it is also closed under countable intersections.

Thence, by definition, $\Sigma$ is a monotone class.