Category:Definitions/Concentration on Measurable Set

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This category contains definitions related to Concentration on Measurable Set.
Related results can be found in Category: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:

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