Definition:Probability Measure

Definition
Let $\mathcal E$ be an experiment.

Let $\Omega$ be the sample space on $\mathcal E$, and let $\Sigma$ be the event space of $\mathcal E$.

A probability measure on $\mathcal E$ is a mapping $\Pr: \Sigma \to \R$ which fulfils the Kolmogorov axioms.

Kolmogorov Axioms
The Kolmogorov axioms are as follows:

Also known as
In the context of probability theory, a probability measure is sometimes referred to as a probability function.

Also see

 * Definition:Probability Space


 * Elementary Properties of Probability Measure