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Additivity, subadditivity and linearity: automatic continuity and quantifier weakening
File | Description | Size | Format | |
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1405.3948.pdf | Accepted version | 301.74 kB | Adobe PDF | View/Open |
Title: | Additivity, subadditivity and linearity: automatic continuity and quantifier weakening |
Authors: | Bingham, NH Ostaszewski, AJ |
Item Type: | Journal Article |
Abstract: | We study the interplay between additivity (as in the Cauchy functional equation), subadditivity and linearity. We obtain automatic continuity results in which additive or subadditive functions, under minimal regularity conditions, are continuous and so linear. We apply our results in the context of quantifier weakening in the theory of regular variation, completing our programme of reducing the number of hard proofs there to zero. |
Issue Date: | 1-Apr-2018 |
Date of Acceptance: | 27-Nov-2017 |
URI: | http://hdl.handle.net/10044/1/63298 |
DOI: | https://dx.doi.org/10.1016/j.indag.2017.11.005 |
ISSN: | 0019-3577 |
Publisher: | Elsevier |
Start Page: | 687 |
End Page: | 713 |
Journal / Book Title: | Indagationes Mathematicae |
Volume: | 29 |
Issue: | 2 |
Copyright Statement: | © 2017 Elsevier Ltd. All rights reserved. This manuscript is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International Licence http://creativecommons.org/licenses/by-nc-nd/4.0/ |
Keywords: | Science & Technology Physical Sciences Mathematics Subadditive Sublinear Shift-compact Analytic spanning set Additive subgroup Hamel basis Steinhaus sum theorem Heiberg-Seneta conditions Thinning Regular variation ABELIAN POLISH GROUPS HAAR MEAGER SETS REGULAR VARIATION INFINITE COMBINATORICS PICCARDS TYPE NULL SETS THEOREM EXTENSIONS LEBESGUE INEQUALITY 0101 Pure Mathematics General Mathematics |
Publication Status: | Published |
Online Publication Date: | 2017-12-06 |
Appears in Collections: | Financial Mathematics Faculty of Natural Sciences Mathematics |