# Definition:Probability Measure/Definition 3

## Definition

Let $\EE$ be an experiment.

Let $\Omega$ be the sample space on $\EE$.

Let $\Sigma$ be the event space of $\mathcal E$.

A probability measure on $\EE$ is a mapping $\Pr: \Sigma \to \R$ which fulfils the following axioms:

 $(\text I)$ $:$ $\ds \forall A \in \Sigma:$ $\ds \map \Pr A$ $\ds \ge$ $\ds 0$ $(\text {II})$ $:$ $\ds \map \Pr \Omega$ $\ds =$ $\ds 1$ $(\text {III})$ $:$ $\ds \forall A \in \Sigma:$ $\ds \map \Pr A$ $\ds =$ $\ds \sum_{\bigcup \set e \mathop = A} \map \Pr {\set e}$ where $e$ denotes the elementary events of $\EE$