Measure is Monotone

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

Then $\mu$ is monotone, that is:
 * $\forall E, F \in \Sigma: E \subseteq F \implies \map \mu E \le \map \mu F$

Proof
A direct corollary of Non-Negative Additive Function is Monotone.