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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
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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 , Proc. Amer. Math. Soc. 112 (1991), 549-562. MR 1036982 (92d:58093)
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- C. Berge, Graphs and hypergraphs, North-Holland, Amsterdam, 1973. MR 0357172 (50:9640)
- [3]
- G. A. Edgar, Measure, topology, and fractal geometry, Springer-Verlag, New York, 1990. MR 1065392 (92a:54001)
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- K. J. Falconer, The geometry of fractal sets, Cambridge Univ. Press, 1985; Fractal geometry, Wiley, New York, 1990. MR 867284 (88d:28001)
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- M. Hata, On the structure of self-similar sets, Japan J. Appl. Math. 2 (1985), 381-414. MR 839336 (87g:58080)
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- J. E. Hutchinson, Fractals and self-similarity, Indiana Univ. Math. J. 30 (1981), 713-747. MR 625600 (82h:49026)
- [7]
- P. A. P. Moran, Additive functions of intervals and Hausdorff measure, Proc. Cambridge Philos. Soc. 42 (1946), 15-23. MR 0014397 (7:278f)
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Additional Information
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
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