Very slowly varying functions. II

N. H. Bingham; A. J. Ostaszewski

Colloquium Mathematicae (2009)

  • Volume: 116, Issue: 1, page 105-117
  • ISSN: 0010-1354

Abstract

top
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.

How to cite

top

N. H. Bingham, and A. J. Ostaszewski. "Very slowly varying functions. II." Colloquium Mathematicae 116.1 (2009): 105-117. <http://eudml.org/doc/283808>.

@article{N2009,
abstract = {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.},
author = {N. H. Bingham, A. J. Ostaszewski},
journal = {Colloquium Mathematicae},
keywords = {regular variation; slow variation; uniform convergence; Heiberg-Lipschitz condition; Heiberg-Seneta theorem},
language = {eng},
number = {1},
pages = {105-117},
title = {Very slowly varying functions. II},
url = {http://eudml.org/doc/283808},
volume = {116},
year = {2009},
}

TY - JOUR
AU - N. H. Bingham
AU - A. J. Ostaszewski
TI - Very slowly varying functions. II
JO - Colloquium Mathematicae
PY - 2009
VL - 116
IS - 1
SP - 105
EP - 117
AB - 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.
LA - eng
KW - regular variation; slow variation; uniform convergence; Heiberg-Lipschitz condition; Heiberg-Seneta theorem
UR - http://eudml.org/doc/283808
ER -

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.