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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



The Lusin-Privalov theorem
for subharmonic functions

Author: Stephen J. Gardiner
Journal: Proc. Amer. Math. Soc. 124 (1996), 3721-3727
MSC (1991): Primary 31B25
MathSciNet review: 1396977
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Abstract: This paper establishes a generalization of the Lusin-Privalov radial uniqueness theorem which applies to subharmonic functions in all dimensions. In particular, it answers a question of Rippon by showing that no subharmonic function on the upper half-space can have normal limit $-\infty $ at every boundary point.

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Stephen J. Gardiner
Affiliation: Department of Mathematics, University College, Dublin 4, Ireland

Received by editor(s): May 10, 1995
Communicated by: Albert Baernstein II
Article copyright: © Copyright 1996 American Mathematical Society