$mu$ pure point measure if and only if $mu(A)=sum_{xin A} mu(left{xright})$
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$mu$ is a pure point measure if and only if for every $Ain mathcal{B}(X)$ , $mathcal{B}(X)$ sigma-algebra Baire. $X$ compact hausdorff $mu(A)=sum_{xin A} mu(left{xright})$ I have this If $mu(A)=0$ is hold. If $mu(A)>0$ , then exists $xin A: mu(left{xright})>0$ Then $left{x:mu(A)>0right}=bigcup_{xin A} left{x:mu(left{xright})>0right}$ and I do not know how to continue ...
real-analysis functional-analysis measure-theory
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asked Nov 17 at 3:10
eraldcoil
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