Definition:Event/Occurrence

Definition
Let the probability space of an experiment $\EE$ be $\struct {\Omega, \Sigma, \Pr}$.

Let $A, B \in \Sigma$ be events, so that $A \subseteq \Omega$ and $B \subseteq \Omega$.

Let the outcome of the experiment be $\omega \in \Omega$.

Then the following real-world interpretations of the occurrence of events can be determined:


 * If $\omega \in A$, then $A$ occurs.


 * If $\omega \notin A$, that is $\omega \in \Omega \setminus A$, then $A$ does not occur.

Also known as
The word happen is often used for occur, and it can be argued that it is easier to understand what is meant.

Also see

 * Definition:Disjoint Events
 * Definition:Complementary Event