Pointwise Product of Measurable Functions is Measurable

Theorem
Let $\left({X, \Sigma}\right)$ be a measurable space.

Let $f, g: X \to \overline{\R}$ be $\Sigma$-measurable functions.

Then the pointwise product $f \cdot g: X \to \overline{\R}$ is also $\Sigma$-measurable.