Measure is Monotone

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

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

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