Bingham, N. H. and Ostaszewski, A. J. 
ORCID: 0000-0003-2630-8663
(2010)
Automatic continuity via analytic thinning.
Proceedings of the American Mathematical Society, 138 (03).
p. 907.
ISSN 0002-9939
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 |
| Divisions: | Mathematics |
| Subjects: | Q Science > QA Mathematics |
| Date Deposited: | 01 Dec 2010 12:23 |
| Last Modified: | 11 Dec 2024 23:42 |
| URI: | http://eprints.lse.ac.uk/id/eprint/29593 |
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