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Foundations of regular variation

By N. H. Bingham and Adam Ostaszewski

Abstract

The theory of regular variation is largely complete in one dimen- sion, but is developed under regularity or smoothness assumptions. For functions of a real variable, Lebesgue measurability su¢ ces, and so does having the property of Baire. We nd here that the preceding two properties have two kinds of common generalization, both of a combinatorial nature; one is exempli ed by �containment up to trans- lation of subsequences�, the other, drawn from descriptive set theory, requires non-emptiness of a Souslin 1 2 -set. All of our generalizations are equivalent to the uniform convergence propert

Topics: QA Mathematics
Publisher: Centre for Discrete and Applicable Mathematics, London School of Economics and Political Science
Year: 2006
OAI identifier: oai:eprints.lse.ac.uk:13797
Provided by: LSE Research Online
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