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An initial concept in a probability model. In the definition of a probability space <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/e/e035/e035310/e0353101.png" /> the non-empty set <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/e/e035/e035310/e0353102.png" /> is called the space of elementary events and any point <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/e/e035/e035310/e0353103.png" /> is an elementary event. In an informal approach, <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/e/e035/e035310/e0353104.png" /> describes the set of all outcomes of a certain random experiment and an elementary event <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/e/e035/e035310/e0353105.png" /> 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 <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/e/e035/e035310/e0353106.png" />, a point of <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/e/e035/e035310/e0353107.png" />, and the event <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/e/e035/e035310/e0353108.png" />, an element of a certain class of sets <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/e/e035/e035310/e0353109.png" />. See [[Probability theory|Probability theory]]; [[Probability space|Probability space]]; [[Random event|Random event]].
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An initial concept in a probability model. In the definition of a probability space $  ( \Omega , {\mathcal A} , {\mathsf P} ) $
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the non-empty set $  \Omega $
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is called the space of elementary events and any point $  \omega \in \Omega $
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is an elementary event. In an informal approach, $  \Omega $
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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 $,  
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a point of $  \Omega $,  
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and the event $  \{ \omega \} $,  
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an element of a certain class of sets $  {\mathcal A} $.  
 +
See [[Probability theory|Probability theory]]; [[Probability space|Probability space]]; [[Random event|Random event]].

Latest revision as of 19:37, 5 June 2020


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