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Meromorphic functions with shared limit values of positive linear measure

Part of: Entire and meromorphic functions, and related topics

Published online by Cambridge University Press:  02 February 2009

Andreas Sauer
Andreas Sauer
Affiliation:
Fachhochschule-Dortmund, Sonnenstrasse 96, 44047 Dortmund, Germany (andreas.sauer@fh-dortmund.de)
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Abstract

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We prove that if two transcendental meromorphic functions share all limit values from a set of positive linear measure on a rectifiable Jordan arc, then they share all limit values.

Keywords

Casorati–Weierstrass theoremshared limit valueslimit uniqueness setlinear measure

MSC classification

Secondary: 30D30: Meromorphic functions, general theory 30D35: Distribution of values, Nevanlinna theory 30D40: Cluster sets, prime ends, boundary behavior
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 52 , Issue 1 , February 2009 , pp. 235 - 240
Copyright
Copyright © Edinburgh Mathematical Society 2009