probability measure

A probability measure is a real-valued function from an event space to the interval $[0,1]$ that satisfies the properties of a measure, i.e. every event has some notion of "size" which can be combined.

Formally,
given an event space $\mathcal{F}$ on sample space $\mathrm{\Omega }$,
a measure $P:\mathcal{F}\to [0,1]$ is a probability measure if

• $P\in [0,1]$, with $P(\varnothing )=0$
• $P\left(\bigcup _{k=1}^{\mathrm{\infty }}{E}_k\right)=\sum _{k=1}^{\mathrm{\infty }}P(E_k)$ for any countable collection of disjoint sets
• $P(A\mid B)=\frac{P(A\cap B)}{P(B)}$ in the case of conditional probability