The Azimuth Project
Probability space (Rev #1, changes)

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Contents

Definition

A probability space consists of the following data:

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

  • The event algebra AA, where each event consists of a set of outcomes in SS, and the collection of events constitutes a σ\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 AA.

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