Centre for Discrete and Applicable Mathematics

CDAM Research Report, LSE-CDAM-2007-03

January 2007 (Revised June 2007)

Very Slowly Varying Functions -- II

N. H. Bingham and A. J. Ostaszewski

This paper is a sequel to both Ash, Erdös and Rubel AER, on very slowly varying functions, and BOst1, on foundations of regular variation. We show that generalizations of the Ash-Erdös-Rubel approach -- imposing growth restrictions on the function h, rather than regularity conditions such as measurability or the Baire property -- lead naturally to the main result of regular variation, the Uniform Convergence Theorem.
Keywords: Slow variation, Uniform Convergence Theorem, Heiberg-Lipschitz condition, Heiberg-Seneta theorem.

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