Boundary limits of Green potentials in the unit disc (Q802051)

We prove the following: let \(\mu\) be a positive Borel measure on the open unit disc D such that \(\log | z| \in L^ 1(\mu)\) and let U(z) be the positive superharmonic function on D given by \(U(z)=\int_{D}| (1-z\xi)/(z-\xi)| d\mu (\xi).\) If \(\gamma\) : [0,1)\(\to D\) is any curve with \(\lim_{t\to 1}\gamma (t)=1\), then \(\lim \inf_{t\to 1}(1- | \gamma (t)|)U(\gamma (t)e^{i\theta})=0\) for all \(\theta\), \(0\leq \theta <2\pi\).