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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)


The strong open set condition
in the random case

Author: Norbert Patzschke
Journal: Proc. Amer. Math. Soc. 125 (1997), 2119-2125
MSC (1991): Primary 28A80; Secondary 60D05, 60G57
MathSciNet review: 1377002
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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.

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Additional Information

Norbert Patzschke
Affiliation: Fakultät für Mathematik und Informatik, Friedrich–Schiller–Universität Jena, D–07740 Jena, Germany

PII: S 0002-9939(97)03816-1
Keywords: Random fractals, (strong) open set condition, multifractals
Received by editor(s): January 16, 1996
Received by editor(s) in revised form: February 7, 1996
Communicated by: Palle E. T. Jorgensen
Article copyright: © Copyright 1997 American Mathematical Society

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