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Automatic continuity via analytic thinning

Bingham, N. H. and Ostaszewski, A. J. (2010) Automatic continuity via analytic thinning. Proceedings of the American Mathematical Society, 138 (03). p. 907. ISSN 0002-9939

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Abstract

We use Choquet's analytic capacitability theorem and the Kestelman-Borwein-Ditor theorem (on the inclusion of null sequences by translation) to derive results on `analytic automaticity' - for instance, a stronger common generalization of the Jones/Kominek theorems that an additive function whose restriction is continuous/bounded on an analytic set $ T$ spanning $ \mathbb{R}$ (e.g., containing a Hamel basis) is continuous on $ \mathbb{R}$. We obtain results on `compact spannability' - the ability of compact sets to span $ \mathbb{R}$. From this, we derive Jones' Theorem from Kominek's. We cite several applications, including the Uniform Convergence Theorem of regular variation.

Item Type: Article
Official URL: http://www.ams.org/publications/journals/journalsf...
Additional Information: © 2010 American Mathematical Association
Library of Congress subject classification: Q Science > QA Mathematics
Sets: Departments > Mathematics
Rights: http://www.lse.ac.uk/library/usingTheLibrary/academicSupport/OA/depositYourResearch.aspx
Date Deposited: 01 Dec 2010 12:23
URL: http://eprints.lse.ac.uk/29593/

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