# Probability space

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 sets containing one element of S are not necessarily events.