Beyond Lebesgue and Baire: generic regular variation

Volume 116 / 2009

N. H. Bingham, A. J. Ostaszewski Colloquium Mathematicum 116 (2009), 119-138 MSC: Primary 26A03. DOI: 10.4064/cm116-1-6

Abstract

We show that the No Trumps combinatorial property (NT), introduced for the study of the foundations of regular variation by the authors, permits a natural extension of the definition of the class of functions of regular variation, including the measurable/Baire functions to which the classical theory restricts itself. The “generic functions of regular variation” defined here characterize the maximal class of functions to which the three fundamental theorems of regular variation (Uniform Convergence, Representation and Characterization Theorems) apply. The proof uses combinatorial variants of the Steinhaus and Ostrowski Theorems deduced from NT in an earlier paper of the authors.

Authors

  • N. H. BinghamMathematics Department
    Imperial College London
    London SW7 2AZ, UK
    e-mail
  • A. J. OstaszewskiMathematics Department
    London School of Economics
    Houghton Street
    London WC2A 2AE, UK
    e-mail

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