Definition (Concentrated)

A Measure $\mu$ on $(X,\mathscr{M},\mu)$ is said to be concentrated on $A\in\mathscr{M}$ if and only if$$\begin{gather*} \forall E\in\mathscr{M}:\mu(E)=\mu(E\cap A)\\ \iff\\ \forall E\in\mathscr{M}:E\cap A=\emptyset:\mu(E)=0 \end{gather*}$$