Displaying similar documents to “Regular variation for measures on metric spaces.”

Very slowly varying functions. II

N. H. Bingham, A. J. Ostaszewski (2009)

Colloquium Mathematicae

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This paper is a sequel to papers by Ash, Erdős and Rubel, on very slowly varying functions, and by Bingham and Ostaszewski, on foundations of regular variation. We show that generalizations of the Ash-Erdős-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.