Category:Definitions/Absolutely Continuous Signed Measures

This category contains definitions related to Absolutely Continuous Signed Measures.
Related results can be found in Category:Absolutely Continuous Signed Measures.

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

Let $\mu$ be a measure on $\struct {X, \Sigma}$.

Let $\nu$ be a signed measure on $\struct {X, \Sigma}$.

Let $\size \nu$ be the variation of $\nu$.

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

$\size \nu$ is absolutely continuous with respect to $\mu$.

We write:

$\nu \ll \mu$