Probability Measure

Statements

Definition. Let $(\Omega ,\mathcal{F},P)$ be a measure space. The measure $P:\mathcal{F}\to [0,1]$ is said to be a probability measure if $P(\varnothing )=0$ and $P(\Omega )=1$. When $P$ is a probability measure, the triple $(\Omega ,\mathcal{F},P)$ is said to be a probability triple or a probability space.