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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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A radial uniqueness theorem for meromorphic functions
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by P. J. Rippon PDF
Proc. Amer. Math. Soc. 85 (1982), 572-574 Request permission

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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Additional Information
  • © Copyright 1982 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 85 (1982), 572-574
  • MSC: Primary 30D40
  • DOI: https://doi.org/10.1090/S0002-9939-1982-0660607-2
  • MathSciNet review: 660607