Theorem of Bartle, Dunford, and Schwartz concerning vector measures

We show the existence, for an arbitrary vector measure $\mu:\Sigma\to X$ (where $X$ is a Banach space and $\Sigma$ is a $\sigma$-algebra of subsets of a set $S$) of a functional $x'\in X'$ ($X'$ is the conjugate space of $X$) such that $\mu$ is absolutely continuous with respect to $\mu_{x'}$, $\mu_{x'}(E)=<x', \mu(E)>$, $E\in\Sigma$.