Uniformity and self-neglecting functions

Abstract

We relax the continuity assumption in Bloom's uniform convergence theorem for Beurling slowly varying functions ϕ. We assume that ϕhas the Darboux property, and obtain results for ϕmeasurable or having the Baire property.

References in corpus (1)

• Kingman, category and combinatorics

Cited by in corpus (1)

• Cauchy's functional equation and extensions: Goldie's equation and inequality, the Gołąb-Schinzel equation and Beurling's equation