# Elementary events

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An initial concept in a probability model. In the definition of a probability space $( \Omega , {\mathcal A} , {\mathsf P} )$ the non-empty set $\Omega$ is called the space of elementary events and any point $\omega \in \Omega$ is an elementary event. In an informal approach, $\Omega$ describes the set of all outcomes of a certain random experiment and an elementary event $\omega$ corresponds to an elementary outcome: the experiment ends with one and only one elementary outcome, these outcomes are indecomposable and mutually exclusive. There is a fundamental difference between an elementary event $\omega$, a point of $\Omega$, and the event $\{ \omega \}$, an element of a certain class of sets ${\mathcal A}$. See Probability theory; Probability space; Random event.

How to Cite This Entry:
Elementary events. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Elementary_events&oldid=46801
This article was adapted from an original article by A.V. Prokhorov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article