suppose $\mu$ is a Radon measure on $X$ such that $\mu(\{x\})=0$ for all $x\in X$, and $A$ is a Borel set in X such that $0<\mu(A)<\infty$. Then show that any $\alpha$ such that $0<\alpha<\mu(A)$, there is a Borel set $B \subset A$ such that $\mu(B)=\alpha$.