Uniformity and self-neglecting functions

2013/01/24 by Bingham, N. H., Ostaszewski, A. J.
#26A03 #33B99 #34D05 #39B22 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1301.5894

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.

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