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 Monotone.

$\blacksquare$