Definition:Concentration on Measurable Set/Signed Measure/Definition 2

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 $E$ :


 * for every $\Sigma$-measurable set $A \subseteq E^c$, we have $\map \mu A = 0$.