Beyond Lebesgue and Baire: generic regular variation

• Autorzy: N. H. Bingham , A. J. Ostaszewski
• Języki publikacji: EN

Abstrakty

EN

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, Representation and Characterization Theorems) apply. The proof uses combinatorial variants of the Steinhaus and Ostrowski Theorems deduced from NT in an earlier paper of the authors.

Kategorie tematyczne

• 26A03: Foundations: limits and generalizations, elementary topology of the line

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2009
• Tom: 116
• Numer: 1
• Strony: 119-138

Daty

wydano

2009

Twórcy

autor

N. H. Bingham

• Mathematics Department, Imperial College London, London SW7 2AZ, UK

autor

A. J. Ostaszewski

• Mathematics Department, London School of Economics, Houghton Street, London WC2A 2AE, UK

Identyfikatory

DOI

10.4064/cm116-1-6