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.