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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
DOI: https://doi.org/10.1090/S0002-9939-1992-1100644-3
MathSciNet review: 1100644
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Abstract | References | Similar Articles | Additional Information

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".


References [Enhancements On Off] (What's this?)

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DOI: https://doi.org/10.1090/S0002-9939-1992-1100644-3
Article copyright: © Copyright 1992 American Mathematical Society

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