@unpublished{Kreitmeier2007, author = {Kreitmeier, Wolfgang}, title = {Asymptotic order of quantization for Cantor distributions in terms of Euler characteristic, Hausdorff and Packing measure}, url = {http://nbn-resolving.de/urn:nbn:de:bvb:739-opus-7374}, year = {2007}, abstract = {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of these sets and the high-rate asymptotics of the quantization error.}, subject = {Maßtheorie}, language = {en} } @unpublished{Kreitmeier2007, author = {Kreitmeier, Wolfgang}, title = {Optimal quantization of probabilities concentrated on small balls}, url = {http://nbn-resolving.de/urn:nbn:de:bvb:739-opus-12010}, year = {2007}, abstract = {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.}, subject = {Maßtheorie}, language = {en} }