# Contents * the following line creates the automatic table of contents {:toc} ## 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 $S$. category:statistical methods