Variants on the Berz sublinearity theorem
File(s)
Published version
Author(s)
Bingham, Nicholas
Ostaszewski, Adam
Type
Journal Article
Abstract
We consider variants on the classical Berz sublinearity theorem, using only DC, the Axiom of Dependent Choices, rather than AC, the Axiom of Choice, which Berz used. We consider thinned versions, in which conditions are imposed on only part of the domain of the function—results of quantifier-weakening type. There are connections with classical results on subadditivity. We close with a discussion of the extensive related literature.
Date Issued
2019-04
Date Acceptance
2018-09-19
Citation
Aequationes Mathematicae, 2019, 93 (2), pp.351-369
ISSN
0001-9054
Publisher
Springer Verlag
Start Page
351
End Page
369
Journal / Book Title
Aequationes Mathematicae
Volume
93
Issue
2
Copyright Statement
© The Author(s) 2018. This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
Subjects
Science & Technology
Physical Sciences
Mathematics, Applied
Mathematics
Dependent Choices
Homomorphism extension
Subadditivity
Sublinearity
Steinhaus-Weil property
Thinning
Quantifier weakening
HAHN-BANACH THEOREM
HAAR NULL SETS
PICCARDS TYPE
STEINHAUS
PROPERTY
AXIOM
0101 Pure Mathematics
General Mathematics
Publication Status
Published
Date Publish Online
2018-11-16