Contents

Definition

A probability space consists of the following data:

• The sample space $S$, which is the set of possible outcomes (of an experiment)

• The event algebra $A$, where each event consists of a set of outcomes in $S$, and the collection of events constitutes a $\sigma$-algebra – it is closed under countable sequences of union, intersection and complement operations (and also set differences). Implied here is the fact that the empty set and whole sample space are events in $A$.

• A measure function $P$, which assigns a probability to each event in $A$. P must be additive on countable disjoint unions, and must assign 1 to the whole sample space $S$.