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

 

Generic subadditive functions


Authors: N. H. Bingham and A. J. Ostaszewski
Journal: Proc. Amer. Math. Soc. 136 (2008), 4257-4266
MSC (2000): Primary 39B62
Published electronically: July 22, 2008
MathSciNet review: 2431038
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Abstract: We prove a generalization of the `Subadditive Limit Theorem' and of the corresponding Berz Theorem in a class of functions that includes both the measurable functions and the `Baire functions'. The generic subadditive functions are defined by a combinatorial property previously introduced by the authors for the study of the foundations of regular variation. By specialization we provide the previously unknown Baire variants of the fundamental theorems of subadditive functions, answering an old question posed by Bingham, Goldie, and Teugels in 1987.


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Additional Information

N. H. Bingham
Affiliation: Department of Mathematics, Imperial College London, South Kensington, London SW7 2AZ, United Kingdom
Email: n.bingham@ic.ac.uk

A. J. Ostaszewski
Affiliation: Department of Mathematics, London School of Economics, Houghton Street, London WC2A 2AE, United Kingdom
Email: a.j.ostaszewski@lse.ac.uk

DOI: http://dx.doi.org/10.1090/S0002-9939-08-09504-X
PII: S 0002-9939(08)09504-X
Keywords: No trumps principle, subadditive function.
Received by editor(s): June 29, 2007
Published electronically: July 22, 2008
Communicated by: Michael T. Lacey
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.