Uniformity and self-neglecting functions: II. Beurling Regular Variation and the class Γ

2013/07/19 by Ν. H. Bingham, Bingham, N. H., A. J. Ostaszewski +1
Computer Science · Mathematics · #26A03 #33B99 #34D05 #39B22 #Advanced Topology and Set Theory #Classical Analysis and ODEs (math.CA) #Computability, Logic, AI Algorithms #FOS: Mathematics #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.1307.5305

openalex publication_date 2013/07/19 · openalex created_date 2024/04/10 · openalex updated_date 2026/07/28

Abstract

Beurling slow variation is generalized to Beurling regular variation. A Uniform Convergence Theorem, not previously known, is proved for those functions of this class that are measurable or have the Baire property. This permits their characterization and representation. This extends the gamma class of de Haan theory studied earlier.

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