Definition:Event

Context
Probability Theory.

Definition
Let $$\mathcal E$$ be an experiment.

An event in $$\mathcal E$$ is an element of the event space $$\Sigma$$ of $$\mathcal E$$.

Occurrence
Let the probability space of an experiment $$\mathcal E$$ be $$\left({\Omega, \Sigma, \Pr}\right)$$.

Let $$A \in \Sigma$$, so that $$A \subseteq \Omega$$.

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

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

If $$\omega \notin A$$, then $$A$$ does not occur.