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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Sub-self-similar sets


Author: K. J. Falconer
Journal: Trans. Amer. Math. Soc. 347 (1995), 3121-3129
MSC: Primary 28A80; Secondary 28A78
DOI: https://doi.org/10.1090/S0002-9947-1995-1264809-X
MathSciNet review: 1264809
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Abstract: A compact set $ E \subseteq {{\mathbf{R}}^n}$ is called sub-self-similar if $ E \subseteq \bigcup\nolimits_{i = 1}^m {{S_i}(E)} $, where the $ {S_i}$ are similarity transfunctions. We consider various examples and constructions of such sets and obtain formulae for their Hausdorff and box dimensions, generalising those for self-similar sets.


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DOI: https://doi.org/10.1090/S0002-9947-1995-1264809-X
Article copyright: © Copyright 1995 American Mathematical Society