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

N. H. Bingham¹ ; A. J. Ostaszewski²

¹ Mathematics Department Imperial College London London SW7 2AZ, UK
² Mathematics Department London School of Economics Houghton Street London WC2A 2AE, UK

Colloquium Mathematicum, Tome 121 (2010) no. 2, pp. 225-238

Résumé

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.

Détail

DOI : 10.4064/cm121-2-5

Keywords: re examine measure category duality bitopological approach using euclidean density topologies line topological result convergence homeomorphisms identity obtaining corollary results infinitary combinatorics due kestelman borwein ditor hence unified proof measure category cases uniform convergence theorem slowly varying functions extend results slowly varying functions ash erd rubel