Uniformity and self-neglecting functions
Classical Analysis and ODEs
2013-01-25 v1 Probability
Abstract
We relax the continuity assumption in Bloom's uniform convergence theorem for Beurling slowly varying functions \phi. We assume that \phi has the Darboux property, and obtain results for \phi measurable or having the Baire property.
Cite
@article{arxiv.1301.5894,
title = {Uniformity and self-neglecting functions},
author = {N. H. Bingham and A. J. Ostaszewski},
journal= {arXiv preprint arXiv:1301.5894},
year = {2013}
}