Additivity, subadditivity and linearity: automatic continuity and quantifier weakening
File(s)
Accepted version
Author(s)
Bingham, NH
Ostaszewski, AJ
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.
Date Issued
2018-04-01
Date Acceptance
2017-11-27
Citation
Indagationes Mathematicae, 2018, 29 (2), pp.687-713
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/
Identifier
http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000429511400011&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=1ba7043ffcc86c417c072aa74d649202
Subjects
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
Publication Status
Published
Date Publish Online
2017-12-06