https://en.wikipedia.org/wiki/Probability_space

1. A Measurable space
   1. A Set, called the Sample space, $\Omega$, which is the set of all possible outcomes.
   2. A Sigma-algebra, referred to as the set of events $\mathcal{F}$, where each event is a set containing zero or more outcomes.
2. A Probability measure, which corresponds to the assignment of probabilities to the events; that is, a function $P$ from events to probabilities.