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International Journal of Mathematics and Mathematical Sciences
Volume 31 (2002), Issue 1, Pages 23-29
http://dx.doi.org/10.1155/S0161171202110398

Asymptotic Hölder absolute values

Department of Mathematics, University of California, Los Angeles, 405 Hilgard Avenue, Los Angeles 90095-1555, CA, USA

Received 12 October 2001

Copyright © 2002 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We prove that asymptotic Hölder absolute values are Hölder equivalent to classical absolute values. As a corollary we obtain a generalization of Ostrowski's theorem and a classical theorem by E. Artin. The theorem presented implies a new, more flexible, definition of classical absolute value.