Definition:Event Space/Discrete

Definition
Let $\mathcal E$ be an experiment.

Let $\Omega$ be a discrete sample space of $\mathcal E$.

Then it is usual to take $\Sigma$ to be the power set $\mathcal P \left({\Omega}\right)$ of $\Omega$, that is, the set of all possible subsets of $\Omega$.

Also see

 * Power Set of Sample Space is an Event Space for a demonstration that this is a valid approach.