The strong open set condition in the random case
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- by Norbert Patzschke PDF
- Proc. Amer. Math. Soc. 125 (1997), 2119-2125 Request permission
Abstract:
To describe some fractal properties of a self–similar set or measure, such as the Hausdorff dimension and the multifractal spectrum, it is useful that it satisfy the strong open set condition, which means there is an open set satisfying the open set condition and, additionally, a part of the self–similar set must meet the open set. It is known that in the non–random case the strong open set condition and the open set condition are equivalent. This paper treats the random case. If the open set condition is assumed, we show that there is a random open set satisfying the strong open set condition. Further, we give an application to multifractal analysis of the random self–similar fractal.References
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Additional Information
- Norbert Patzschke
- Affiliation: Fakultät für Mathematik und Informatik, Friedrich–Schiller–Universität Jena, D–07740 Jena, Germany
- Email: patzschke@minet.uni-jena.de
- Received by editor(s): January 16, 1996
- Received by editor(s) in revised form: February 7, 1996
- Communicated by: Palle E. T. Jorgensen
- © Copyright 1997 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 125 (1997), 2119-2125
- MSC (1991): Primary 28A80; Secondary 60D05, 60G57
- DOI: https://doi.org/10.1090/S0002-9939-97-03816-1
- MathSciNet review: 1377002