Very slowly varying functions. II

Volume 116 / 2009

N. H. Bingham, A. J. Ostaszewski Colloquium Mathematicum 116 (2009), 105-117 MSC: Primary 26A03. DOI: 10.4064/cm116-1-5


This paper is a sequel to papers by Ash, Erdős and Rubel, on very slowly varying functions, and by Bingham and Ostaszewski, on foundations of regular variation. We show that generalizations of the Ash–Erdős–Rubel approach—imposing growth restrictions on the function $h$, rather than regularity conditions such as measurability or the Baire property—lead naturally to the main result of regular variation, the Uniform Convergence Theorem.


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

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