Definition:Absolute Continuity/Measure

Definition
Let $\struct {X, \Sigma}$ be a measurable space.

Let $\mu$ and $\nu$ be measures on $\struct {X, \Sigma}$.

We say that $\nu$ is absolutely continuous with respect to $\mu$ and write:


 * $\nu \ll \mu$




 * $\ds \forall A \in \Sigma : \map \mu A = 0 \implies \map \nu A = 0$