Definition 23.4.1 (Absolutely Continuous).label Let $(X, \cm)$ be a measurable space, $\mu$ be a positive measure on $(X, \cm)$, and $\nu$ be a signed measure or vector veasure on $(X, \cm)$, then $\nu$ is absolutely continuous with respect to $\mu$, denoted $\nu \ll \mu$, if for every $E \in \cm$ with $\mu(E) = 0$, $\nu(E) = 0$ as well.