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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Self-similar sets in complete metric spaces


Author: Andreas Schief
Journal: Proc. Amer. Math. Soc. 124 (1996), 481-490
MSC (1991): Primary 28A80, 28A78
DOI: https://doi.org/10.1090/S0002-9939-96-03158-9
MathSciNet review: 1301047
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Abstract: We develop a theory for Hausdorff dimension and measure of self-similar sets in complete metric spaces. This theory differs significantly from the well-known one for Euclidean spaces. The open set condition no longer implies equality of Hausdorff and similarity dimension of self-similar sets and that $K$ has nonzero Hausdorff measure in this dimension. We investigate the relationship between such properties in the general case.


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Additional Information

Andreas Schief
Affiliation: Corporate Research and Development, SIEMENS AG, 81730, Munich, Germany
Email: andreas.schief@zfe.siemens.de

DOI: https://doi.org/10.1090/S0002-9939-96-03158-9
Keywords: SOSC, OSC, self-similar sets, fractals, Hausdorff dimension, complete metric spaces
Received by editor(s): June 9, 1994
Received by editor(s) in revised form: August 23, 1994
Communicated by: Christopher D. Sogge
Article copyright: © Copyright 1996 American Mathematical Society