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The Hausdorff dimension of general Sierpiński carpets

Published online by Cambridge University Press:  22 January 2016

Curt McMullen
Curt McMullen*
Affiliation:
Department of Mathematics, Harvard University, Cambridge Massachusetts 01238, USA
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In this note we determine the Hausdorff dimension of a family of planar sets which are generalizations of the classical Cantor set.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 96 , December 1984 , pp. 1 - 9
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1984

References

[ 1 ] Beardon, A.F., On the Hausdorff dimension of general Cantor sets, Proc. Camb. Phil. Soc, 61 (1965), 679–694.CrossRefGoogle Scholar
[ 2 ] Hironaka, H., Hironaka Heisuke no Suugaku Kyositsu, Tokyo 1980.Google Scholar
[ 3 ] Loeve, Michael, Probability Theory, New York 1963.Google Scholar
[ 4 ] Mandelbrot, Benoit B., Fractals, San Francisco, 1977.Google Scholar
[ 5 ] Parthasarathy, K.R., Probability Measures on Metric Spaces, New York, 1967.Google Scholar
[ 6 ] Sierpiński, W., “Sur une courbe cantorienne qui contient une image biunivoque et continue de toute courbe donné”, Comptes Rendus, 162 (1916), 629–642.Google Scholar
[ 7 ] Wegmann, H., “Die HausdorfF-Dimension von kartesischen Produkten metrischer Räume”, J. Reine Angew. Math., 246 (1971), 46–75.Google Scholar