Baire classification of ...-density and ...-approximately continous functions.
Beyond Lebesgue and Baire: generic regular variation
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,...
Beyond Lebesgue and Baire II: Bitopology and measure-category duality
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...