Let \((\Omega, \mathscr{A}, \mathbb{P})\) be a probability space and let \(\mathbb{P}^{*}(Q):=\inf \{\mathbb{P}(A): A \supset Q, A \in \mathscr{A}\}\) be the outer measure. If \(\Omega_{0} \subset \Omega\) is such that \(\mathbb{P}^{*}\left(\Omega_{0}ight)=1\), then \(\left(\Omega_{0}, \mathscr{A}_{0}, \mathbb{P}_{0}ight)\) with \(\mathscr{A}_{0}:=\Omega_{0} \cap \mathscr{A}\) and \(\mathbb{P}_{0}\left(A_{0}ight):=\mathbb{P}(A)\) for every \(A_{0} \in \mathscr{A}_{0}\) of the form \(A_{0}=\Omega_{0} \cap A\), defines a new probability space.