Bingham, N. H. and Ostaszewski, Adam 
ORCID: 0000-0003-2630-8663
(2007)
Analytic automaticity: the theorems of Jones and Kominek.
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London School of Economics and Political Science, London, UK.
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 |
| Divisions: | Mathematics |
| Subjects: | H Social Sciences > H Social Sciences (General) |
| Date Deposited: | 10 Jul 2008 08:41 |
| Last Modified: | 12 Dec 2024 05:46 |
| URI: | http://eprints.lse.ac.uk/id/eprint/6830 |
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