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Foundations of regular variation

Bingham, N. H. and Ostaszewski, Adam (2006) Foundations of regular variation. CDAM research report, LSE-CDAM-2006-22. Centre for Discrete and Applicable Mathematics, London School of Economics and Political Science, London, UK.

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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 property

Item Type: Monograph (Report)
Official URL: http://www.cdam.lse.ac.uk
Additional Information: © 2006 the authors
Library of Congress subject classification: Q Science > QA Mathematics
Sets: Research centres and groups > Managerial Economics and Strategy Group
Departments > Mathematics
Rights: http://www.lse.ac.uk/library/usingTheLibrary/academicSupport/OA/depositYourResearch.aspx
Identification Number: LSE-CDAM-2006-22
Date Deposited: 13 Oct 2008 14:53
URL: http://eprints.lse.ac.uk/13797/

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