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

Article copyright:
© Copyright 1992
American Mathematical Society