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math.CA2013
Uniformity and self-neglecting functions: II. Beurling Regular Variation and the class Γ
N. H. Bingham, A. J. Ostaszewski
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 meas…
math.CA2013★ 2 cited
Uniformity and self-neglecting functions
N. H. Bingham, A. J. Ostaszewski
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…