Definition 16.3.1 (Absolutely Continuous). Let $(X, \cm)$ be a measurable space and $\mu, \nu$ be signed/vector measures on $X$, then $\nu$ is absolutely continuous with respect to $\mu$, denoted $\nu \ll \mu$, if every $\mu$-null set is $\nu$-null.
Definition 16.3.1 (Absolutely Continuous). Let $(X, \cm)$ be a measurable space and $\mu, \nu$ be signed/vector measures on $X$, then $\nu$ is absolutely continuous with respect to $\mu$, denoted $\nu \ll \mu$, if every $\mu$-null set is $\nu$-null.