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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A radial uniqueness theorem for meromorphic functions


Author: P. J. Rippon
Journal: Proc. Amer. Math. Soc. 85 (1982), 572-574
MSC: Primary 30D40
MathSciNet review: 660607
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Abstract: A classical theorem of Lusin and Privalov states that a meromorphic function in the unit disc, which has radial limit zero on a set which is both of second category and metrically dense in some boundary arc, must vanish identically. We prove below a radial uniqueness theorem which includes the Lusin-Privalov theorem as a special case and which also generalises the Barth-Schneider-Tse asymptotic analogue of the F. and M. Riesz radial uniqueness theorem. The part of the proof relating to Baire category is disposed of by using the Collingwood maximality theorem.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1982-0660607-2
PII: S 0002-9939(1982)0660607-2
Article copyright: © Copyright 1982 American Mathematical Society