Beyond Lebesgue and Baire II: Bitopology and measure-category duality
Volume 121 / 2010
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.
