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Infinite combinatorics in function spaces: category methods

Bingham, N. H. and Ostaszewski, A. J. (2009) Infinite combinatorics in function spaces: category methods. Publications de L’institut Mathématique, Nouvelle Série, 86 (100). pp. 55-73. ISSN 0350-1302

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Abstract

The infinite combinatorics here give statements in which, from some sequence, an infinite subsequence will satisfy some condition – for example, belong to some specified set. Our results give such statements generically – that is, for `nearly all' points, or as we shall say, for quasi all points – all off a null set in the measure case, or all off a meagre set in the category case. The prototypical result here goes back to Kestelman in 1947 and to Borwein and Ditor in the measure case, and can be extended to the category case also. Our main result is what we call the Category Embedding Theorem, which contains the Kestelman–Borwein–Ditor Theorem as a special case. Our main contribution is to obtain functionwise rather than pointwise versions of such results. We thus subsume results in a number of recent and related areas, concerning e.g., additive, subadditive, convex and regularly varying functions.

Item Type: Article
Official URL: http://www.emis.de/journals/PIMB/
Additional Information: © 2009 The Mathematical Institute of SANU
Library of Congress subject classification: Q Science > QA Mathematics
H Social Sciences > HA Statistics
Sets: Departments > Mathematics
Rights: http://www.lse.ac.uk/library/usingTheLibrary/academicSupport/OA/depositYourResearch.aspx
Date Deposited: 31 Mar 2010 13:35
URL: http://eprints.lse.ac.uk/27639/

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