Self-similar sets. VII. A characterization of self-similar fractals with positive Hausdorff measure
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- by Christoph Bandt and Siegfried Graf
- Proc. Amer. Math. Soc. 114 (1992), 995-1001
- DOI: https://doi.org/10.1090/S0002-9939-1992-1100644-3
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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".References
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Bibliographic Information
- © Copyright 1992 American Mathematical Society
- 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