Definition:Concentration on Measurable Set/Signed Measure/Definition 2
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Definition
Let $\struct {X, \Sigma}$ be a measurable space.
Let $\mu$ be a signed measure on $\struct {X, \Sigma}$.
Let $E \in \Sigma$.
We say that $\mu$ is concentrated on $E$ if and only if:
- for every $\Sigma$-measurable set $A \subseteq E^c$, we have $\map \mu A = 0$.
Sources
- 2013: Donald L. Cohn: Measure Theory (2nd ed.) ... (previous) ... (next): $4.3$: Singularity