TY - INPR A1 - Kreitmeier, Wolfgang T1 - Hausdorff measure of uniform self-similar fractals N2 - Let d ≥ 1 be an integer and E a self-similar fractal set, which is the attractor of a uniform contracting iterated function system (UIFS) on Rd. Denote by D the Hausdorff dimension, by HD(E) the Hausdorff measure and by diam (E) the diameter of E. If the UIFS is parametrised by its contracting factor c, while the set ω of fixed points of the UIFS does not depend on c, we will show the existence of a positive constant depending only on ω, such that the Hausdorff dimension is smaller than one and HD = (E) D if c is smaller than this constant. We apply our result to modified versions of various classical fractals. Moreover we present a parametrised UIFS where ω depends on c and HD < diam(E)D, if c is small enough. KW - Maßtheorie KW - Iteriertes Funktionensystem KW - Hausdorff-Dimension KW - Hausdorff-Maß KW - Self-similar set KW - Hausdorff measure Y1 - 2010 UR - https://opus4.kobv.de/opus4-uni-passau/frontdoor/index/index/docId/119 UR - https://nbn-resolving.org/urn:nbn:de:bvb:739-opus-17948 N1 - This is a preprint of an article accepted for publication in Analysis in Theory and Applications ISSN: 1672-4070 (print version) ISSN: 1573-8175 (electronic version) Copyright (c) by Springer. The original publication is available at www.springerlink.com ER -