Beyond Lebesgue and Baire II: Bitopology and measure-category duality

Volume 121 / 2010

N. H. Bingham, A. J. Ostaszewski Colloquium Mathematicum 121 (2010), 225-238 MSC: 26A03, 03E15, 28A05, 54H05. DOI: 10.4064/cm121-2-5

Abstract

We re-examine measure-category duality by a bitopological approach, using both the Euclidean and the density topologies of the line. We give a topological result (on convergence of homeomorphisms to the identity) obtaining as a corollary results on infinitary combinatorics due to Kestelman and to Borwein and Ditor. We hence give a unified proof of the measure and category cases of the Uniform Convergence Theorem for slowly varying functions. We also extend results on very slowly varying functions of Ash, Erdős and Rubel.

Authors

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

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