TY - INPR A1 - Kreitmeier, Wolfgang T1 - Asymptotic order of quantization for Cantor distributions in terms of Euler characteristic, Hausdorff and Packing measure N2 - 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. KW - Maßtheorie KW - Fraktale Dimension KW - Iteriertes Funktionensystem KW - Cantor-Menge KW - Hausdorff-Dimension KW - Hausdorff-Maß KW - Homogeneous Cantor set KW - Euler characteristic KW - Euler exponent KW - quantization dimension KW - quantization coefficient KW - Hausdorff dimension Y1 - 2007 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:bvb:739-opus-7374 N1 - Die Endfassung des Artikels kann beim Verfasser angefordert werden. Kontaktinformation: opus@uni-passau.de ER - TY - INPR A1 - Kreitmeier, Wolfgang T1 - Optimal quantization of probabilities concentrated on small balls N2 - We consider probability distributions which are uniformly distributed on a disjoint union of balls with equal radius. For small enough radius the optimal quantization error is calculated explicitly in terms of the ball centroids. We apply the results to special self-similar measures. KW - Maßtheorie KW - Quantisierung KW - Iteriertes Funktionensystem KW - Schwerpunkt KW - optimal quantization KW - centroid KW - self-similar probabilities Y1 - 2007 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:bvb:739-opus-12010 ER -