# Measure for which it’s logarithmic potential is continuous

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.