Foundations of regular variation

Bingham, N. H. and Ostaszewski, Adam ORCID: 0000-0003-2630-8663 (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
Divisions:	Mathematics
Subjects:	Q Science > QA Mathematics
Date Deposited:	13 Oct 2008 14:53
Last Modified:	12 Dec 2024 05:43
URI:	http://eprints.lse.ac.uk/id/eprint/13797

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