Probability Measure is Monotone

Theorem
Let $$\Pr$$ be a probability measure on an event space $$\Sigma$$.

Then $$\Pr$$ is monotone, that is:


 * $$A, B \in \Sigma: A \subseteq B \implies \Pr \left({A}\right) \le \Pr \left({B}\right)$$.

Proof
As by definition a probability measure is a measure, we can directly use the result Measure is Monotonic.