Definition:Event Space/Discrete

Definition
Let $\EE$ be an experiment.

Let $\Omega$ be a discrete sample space of $\EE$.

Then it is commonplace to take $\Sigma$ to be the power set $\powerset \Omega$ of $\Omega$, that is, the set of all possible subsets of $\Omega$.

Also see

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