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Analytic automaticity: the theorems of Jones and Kominek

Bingham, N. H. and Ostaszewski, Adam (2007) Analytic automaticity: the theorems of Jones and Kominek. LSE-CDAM-2007-24. London school of economics and political science, London, UK.

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Identification Number: LSE-CDAM-2007-24

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 R (e.g., containing a Hamel basis) is continuous on R. We obtain results on `compact spannability' -- the ability of compact sets to span R. From this, we derive Jones' Theorem from Kominek's. We cite several applications including the Uniform Convergence Theorem of regular variation.

Item Type: Monograph (Report)
Official URL: http://www.cdam.lse.ac.uk/Reports/
Additional Information: © 2007 London school of economics and political science
Subjects: H Social Sciences > H Social Sciences (General)
Sets: Departments > Mathematics
Date Deposited: 10 Jul 2008 08:41
Last Modified: 11 May 2011 09:32
URI: http://eprints.lse.ac.uk/id/eprint/6830

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