Self-similar sets in complete metric spaces
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- by Andreas Schief PDF
- Proc. Amer. Math. Soc. 124 (1996), 481-490 Request permission
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.References
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Additional Information
- Andreas Schief
- Affiliation: Corporate Research and Development, SIEMENS AG, 81730, Munich, Germany
- Email: andreas.schief@zfe.siemens.de
- Received by editor(s): June 9, 1994
- Received by editor(s) in revised form: August 23, 1994
- Communicated by: Christopher D. Sogge
- © Copyright 1996 American Mathematical Society
- 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