Category:Absolutely Continuous Measures

This category contains results about absolutely continuous measures.
Definitions specific to this category can be found in Definitions/Absolutely Continuous Measures.

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:

$\nu \ll \mu$

if and only if:

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