Beyond Lebesgue and Baire: generic regular variation

Abstract. We show that the No Trumps combinatorial property (NT), intro-duced for the study of the foundations of regular variation in [BOst1], permits a natural extension of the definition of the class of functions of regular vari-ation, including the measurable/Baire functions to which the classical theory restricts itself. The ‘generic functions of regular variation ’ defined here charac-terize the maximal class of functions, to which the three fundamental theorems of regular variation (Uniform Convergence, Representation and Characteriza-tion Theorems) apply. The proof uses combinatorial variants of the Steinhaus and Ostrowski Theorems deduced from NT in [BOst3].