Additivity, subadditivity and linearity: automatic continuity and quantifier weakening

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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
Mathematics
Faculty of Natural Sciences



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