Differentiation of Radon measures

Question

Assume $\ (X,d)$ is a locally compact metric metric space and $\ \nu,\, \mu$ are Radon measures on $X$. Then, suppose that the following hypothesis hold:

1. $\ w\in L^1_{\mathrm{loc}}(X,\mu),\,w\ge0\,\, \mu- $a.e. on $X$;
2. $\ w$ is continuous in $\ x_0$ and $\mu(B(x_0,r))>0$ for all $\ r>0$;
3. $\ \nu(A)=\int_A w d\mu$ $\forall A\in\mathcal{M}$.

Then I have to prove that there exists $\ \lim_{r\to 0}\frac{\nu(B(x_0,r))}{\mu(B(x_0,r))}=w(x_0)$.