This paper is a sequel to papers by Ash, Erdős and Rubel, on very slowly varying functions, and by Bingham and Ostaszewski, on foundations of regular variation. We show that generalizations of the Ash-Erdős-Rubel approach-imposing growth restrictions on the function h, rather than regularity conditions such as measurability or the Baire property-lead naturally to the main result of regular variation, the Uniform Convergence Theorem.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm116-1-5,
author = {N. H. Bingham and A. J. Ostaszewski},
title = {Very slowly varying functions. II},
journal = {Colloquium Mathematicae},
volume = {116},
year = {2009},
pages = {105-117},
zbl = {1177.26002},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm116-1-5}
}
N. H. Bingham; A. J. Ostaszewski. Very slowly varying functions. II. Colloquium Mathematicae, Tome 116 (2009) pp. 105-117. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm116-1-5/