Proceedings of the American Mathematical Society

Author(s): Stephen J. Gardiner
Journal: Proc. Amer. Math. Soc. 129 (2001), 3379-3387.
MSC (2000): Primary 31B25
Posted: April 25, 2001
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Let

denote the unit ball in $\mathbb{R}^{n}.$ This paper characterizes the subsets

with the property that $\sup_{E}h=\sup_{B}h$ for all harmonic functions

which have finite Dirichlet integral. It also examines, in the spirit of a celebrated paper of Brelot and Doob, the associated question of the connection between non-tangential and fine cluster sets of functions on

at points of the boundary.

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