Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

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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

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