How answer this question? Could be a hint!
Let $(X,M,\rho)$ be a finite measure space. Suppose $U \subset M$ is an algebra of sets and $\mu: U \longrightarrow \mathrm{C}$ is a complex, finitely additive measure such that $|\mu(E)| \leq \rho(E) < \infty$ for all $E \in U.$ Show that there is a complex measure $\nu: M \longrightarrow \mathrm{C},$ whose restriction to $M$ is $\mu$, and such that $|\nu(E)| \leq \rho(R)$, for all $E \in M$.