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

 

Self-similar sets. VII. A characterization of self-similar fractals with positive Hausdorff measure


Authors: Christoph Bandt and Siegfried Graf
Journal: Proc. Amer. Math. Soc. 114 (1992), 995-1001
MSC: Primary 28A80; Secondary 58F08
MathSciNet review: 1100644
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Abstract: For self-similar sets with nonoverlapping pieces, Hausdorff dimension and measure are easily determined. We express "absence of overlap" in terms of discontinuous action of a family of similitudes, thus improving the usual "open set condition".


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DOI: http://dx.doi.org/10.1090/S0002-9939-1992-1100644-3
PII: S 0002-9939(1992)1100644-3
Article copyright: © Copyright 1992 American Mathematical Society