Calculus of Variations and Geometric Measure Theory
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Z. Balogh - H. Rohner

Self-similar sets in doubling spaces

created by zoltan on 13 Aug 2007

[BibTeX]

Accepted Paper

Inserted: 13 aug 2007

Journal: Illinois Journal of Mathematics
Year: 2007

Abstract:

We extend the well-known Moran-Hutchinson Theorem, saying that under the open set condition the Hausdorff dimension of self-similar sets coincides with the similarity dimension, to the more general setting of doubling metric spaces and prove its reverse implication. We also provide examples of iterated function systems in doubling metric spaces where our results apply.

Keywords: Hausdorff dimension, metric spaces, fractal sets


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