# Online Encyclopedia

# Probability space

In mathematics, a **probability space** is a set *S*, together with a σ-algebra *X* on *S* and a measure *P* on that σ-algebra such that *P*(*S*) = 1. The set *S* is called the sample space and the elements of *X* are called the events. The measure *P* is called the *probability measure*, and *P*(*E*) is the probability of the event *E*.

The above is a compact form of stating the probability axioms.

Note that not all subsets of a probability space are events.

Last updated: 10-24-2004 05:10:45