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.
Author: | Wolfgang Kreitmeier |
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URN: | urn:nbn:de:bvb:739-opus-7374 |
Document Type: | Preprint |
Language: | English |
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: | Maßtheorie; Fraktale Dimension; Iteriertes Funktionensystem; Cantor-Menge; Hausdorff-Dimension; Hausdorff-Maß |
Note: | Die Endfassung des Artikels kann beim Verfasser angefordert werden. Kontaktinformation: opus@uni-passau.de |
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: http://www.elsevier.com/. 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): | Standardbedingung laut Einverständniserklärung |