Variants on the Berz sublinearity theorem
Classical Analysis and ODEs
2017-12-15 v1
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.
Keywords
Cite
@article{arxiv.1712.05183,
title = {Variants on the Berz sublinearity theorem},
author = {N. H. Bingham and A. J. Ostaszewski},
journal= {arXiv preprint arXiv:1712.05183},
year = {2017}
}
Comments
Dedication: To Roy O. Davies on his 90-th birthday. Keywords: Dependent Choices, Homomorphism extension, Subadditivity, Sublinearity, Steinhaus-Weil property, Thinning, Quantifier weakening