Constant Function is Measurable

Theorem
Let $\struct {X, \Sigma, \mu}$ be a measure space.

Let $f : X \to \overline \R$ be a constant extended real-valued function.

That is, there exists $c \in \overline \R$ such that:


 * $\map f x = c$ for all $x \in X$.

Then $f$ is $\Sigma$-measurable.