# Elementary events

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