Let $S$ be a set and $\Sigma$ be a $\sigma$-algebra of subsets of $S$. Let $A$ be a Banach space. A countably additive maps $\mu:\Sigma\to A$ is called a vector measure. For any vector measure $\mu$ the semi-variation is defined by
$$
||\mu|| = \sup \left| \sum_i x_i\mu(E_i)\right|,
$$ 
where the supremum extends over all partitions of $S$ into finite number of disjoint sets $\{E_i\}\subset\Sigma$ and all functionals $\{x_i\}\subset A^*$ (the dual of $A$). 

Is it true that $||\mu||$ is a norm in the space of vector measures. If yes, is the space of vector measures equipped with this norm complete.