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Infinite combinatorics and the foundations of regular variation

Bingham, N. H. and Ostaszewski, Adam (2009) Infinite combinatorics and the foundations of regular variation. Journal of Mathematical Analysis and Applications, 360 (2). pp. 518-529. ISSN 0022-247X

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Identification Number: 10.1016/j.jmaa.2009.04.061


The theory of regular variation is largely complete in one dimension, but is developed under regularity or smoothness assumptions. For functions of a real variable, Lebesgue measurability suffices, and so does having the property of Baire. We find here that the preceding two properties have common combinatorial generalizations, exemplified by ‘containment up to translation of subsequences’. All of our combinatorial regularity properties are equivalent to the uniform convergence property.

Item Type: Article
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Additional Information: © 2009 Elsevier B.V.
Divisions: Mathematics
Subjects: Q Science > QA Mathematics
Date Deposited: 15 Dec 2009 15:22
Last Modified: 16 May 2024 00:53

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