I got stuck on a problem on Folland's book, here is the problem:

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.

thank you all!