Generic subadditive functions

Bingham, N.; Ostaszewski, A.

doi:10.1090/S0002-9939-08-09504-X

Generic subadditive functions
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by N. H. Bingham and A. J. Ostaszewski

Proc. Amer. Math. Soc. 136 (2008), 4257-4266

DOI: https://doi.org/10.1090/S0002-9939-08-09504-X

Published electronically: July 22, 2008

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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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