Beyond Lebesgue and Baire: generic regular variation

Abstract

We show that the No Trumps combinatorial property (NT), introduced for the study of the foundations of regular variation in LSE-CDAM-2006-22, 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, Representation and Characterization Theorems) apply. The proof uses combinatorial variants of the Steinhaus and Ostrowski Theorems deduced from NT in LSE-CDAM-2007-15