Category:Concentration on Measurable Set

This category contains results about Concentration on Measurable Set.
Definitions specific to this category can be found in Definitions/Concentration on Measurable Set.

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

Measure

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

Let $E \in \Sigma$.

We say that $\mu$ is concentrated on $E$ if and only if:

$\map \mu {E^c} = 0$

Signed Measure

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

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

Let $E \in \Sigma$.

We say that $\mu$ is concentrated on $E$ if and only if:

$\map {\size \mu} {E^c} = 0$

Complex Measure

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

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

Let $E \in \Sigma$.

We say that $\mu$ is concentrated on $E$ if and only if:

$\map {\size \mu} {E^c} = 0$