Definition:Concentration on Measurable Set/Complex Measure/Definition 1
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Definition
Let $\struct {X, \Sigma}$ be a measurable space.
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:
- $\map {\size \mu} {E^c} = 0$
Sources
- 2013: Donald L. Cohn: Measure Theory (2nd ed.) ... (previous) ... (next): $4.3$: Singularity