Measure is Monotone

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

Then $\mu$ is monotone, that is:
 * $\forall E, F \in \Sigma: E \subseteq F \implies \mu \left({E}\right) \le \mu \left({F}\right)$

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