Let $\mu$ be a compactly supported borel probability measure on $\mathbb C$ then it's logaruthmic potential is,

$P_{\mu}(z)= \int_{\mathbb C} log|z-w|d\mu(w)$

It's well known that $P_\mu$ is subharmonic on $\mathbb C$ and harmonic on (Supp ${\mu}$)$^C$.

In general $P_\mu$ need not be continuous on $\mathbb C$. So under what conditions (necessary and sufficient or at least sufficient) on measure $\mu$, $P_{\mu}$ is continuous?

Thanks for any reference or help.