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Boundary limits of Green potentials in the unit disc. (English) Zbl 0553.31003
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 $$\theta$$, $$0\leq \theta <2\pi$$.

##### MSC:
 31A20 Boundary behavior (theorems of Fatou type, etc.) of harmonic functions in two dimensions 30D50 Blaschke products, etc. (MSC2000)
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