Asymptotic order of quantization for Cantor distributions in terms of Euler characteristic, Hausdorff and Packing measure

  • For homogeneous one-dimensional Cantor sets, which are not necessarily self-similar, we show under some restrictions that the Euler exponent equals the quantization dimension of the uniform distribution on these Cantor sets. Moreover for a special sub-class of these sets we present a linkage between the Hausdorff and the Packing measure of these sets and the high-rate asymptotics of the quantization error.

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Author:Wolfgang Kreitmeier
Document Type:Preprint
Year of Completion:2007
Date of Publication (online):2008/01/02
Publishing Institution:Universität Passau
Release Date:2008/01/02
Tag:Euler characteristic; Euler exponent; Hausdorff dimension; Homogeneous Cantor set; quantization coefficient; quantization dimension
GND Keyword:Cantor-Menge; Fraktale Dimension; Hausdorff-Dimension; Hausdorff-Maß; Iteriertes Funktionensystem; Maßtheorie
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Source:This is a preprint of an article accepted for publication in Journal of Mathematical Analysis and Applications, ISSN: 0022-247X. Copyright (c) by Elsevier. URL: The digital object identifier (DOI) of the definitive article is 10.1016/j.jmaa.2007.12.052
Institutes:Fakultät für Informatik und Mathematik / Mitarbeiter Lehrstuhl/Einrichtung der Fakultät für Informatik und Mathematik
Dewey Decimal Classification:5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik
MSC-Classification:28-XX MEASURE AND INTEGRATION (For analysis on manifolds, see 58-XX) / 28Axx Classical measure theory / 28A78 Hausdorff and packing measures
28-XX MEASURE AND INTEGRATION (For analysis on manifolds, see 58-XX) / 28Axx Classical measure theory / 28A80 Fractals [See also 37Fxx]
open_access (DINI-Set):open_access
Licence (German):License LogoStandardbedingung laut Einverständniserklärung

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