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.