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A converse to the Lusin-Privalov radial uniqueness theorem

Author: Robert D. Berman
Journal: Proc. Amer. Math. Soc. 87 (1983), 103-106
MSC: Primary 30D40
MathSciNet review: 677242
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Abstract: Let $ E$ be a subset of the unit circumference $ C$. If for every nonempty open arc $ A$ of $ C$, the set $ E$ is not both metrically dense and of second category in $ A$, then there exists a nonconstant analytic function $ f$ on the open unit disk $ \Delta $, such that $ {f^ * }(\eta ) = 0$, $ \eta \in E$, where $ {f^ * }$ is the radial limit function of $ f$.

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Keywords: Lusin-Privalov, radial uniqueness
Article copyright: © Copyright 1983 American Mathematical Society