Probability Theory

In probability theory, events are subsets of an underlying set \(\Omega \) . Denote by \(\mathcal {P}(\Omega )\) the set of all subsets of \(\Omega \) , together with the empty set \(\emptyset \) . When \(\Omega \) is not finite, one will not in general take all subsets of \(\Omega \) as possible events but restrict to a family of sets \(\mathcal {C}\subset \mathcal {P}(\Omega )\) , called a sigma-algebra; see Definition 7.5.1.