Let \(\Omega\) be a set with \(\sigma\)-algebra \(\mathcal{A}\) and let \(P\) be a measure on \((\Omega, \mathcal{A})\) such that \(P(\Omega) = 1.\) Then then triple \((\Omega, \mathcal{A}, P)\) is called a probability space.

The universal set \(\Omega\) is called the sample space. Measurable sets \(A \in \mathcal{A}\) are called events. The measure \(P\) is called a probability measure.