Let \((X, \mathscr{A}, \mu)\) be a finite measure space, \(\mathscr{B} \subset \mathscr{A}\) a Boolean algebra (i.e. \(X \in \mathscr{B}, \mathscr{B}\) is stable under the formation of finite unions, intersections and complements) and \(m: \mathscr{B} ightarrow[0, \infty)\) an additive set functions satisfying \(0 \leqslant m(B) \leqslant \mu(B)\). Show that \(m\) is a pre-measure.