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Analytic automaticity: the theorems of Jones and Kominek

By N. H. Bingham and Adam Ostaszewski

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

Topics: H Social Sciences (General)
Publisher: London school of economics and political science
Year: 2007
OAI identifier: oai:eprints.lse.ac.uk:6830
Provided by: LSE Research Online
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