Nagoya Mathematical Journal

The Hausdorff dimension of general Sierpiński carpets

Curt McMullen

Full-text: Open access

Article information

Source
Nagoya Math. J. Volume 96 (1984), 1-9.

Dates
First available in Project Euclid: 14 June 2005

Permanent link to this document
http://projecteuclid.org/euclid.nmj/1118787639

Mathematical Reviews number (MathSciNet)
MR0771063

Zentralblatt MATH identifier
0539.28003

Subjects
Primary: 11K55: Metric theory of other algorithms and expansions; measure and Hausdorff dimension [See also 11N99, 28Dxx]

Citation

McMullen, Curt. The Hausdorff dimension of general Sierpiński carpets. Nagoya Mathematical Journal 96 (1984), 1--9. http://projecteuclid.org/euclid.nmj/1118787639.


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References

  • [1] A. F. Beardon, On the Hausdorff dimension of general Cantor sets, Proc. Camb. Phil. Soc, 61 (1965), 679-694.
  • [2] H. Hironaka, Hironaka Heisuke no Suugaku Kyositsu, Tokyo 1980.
  • [3] Michael Loeve, Probability Theory, New York 1963.
  • [4] Benoit B. Mandelbrot, Fractals, San Francisco, 1977.
  • [5] K. R. Parthasarathy, Probability Measures on Metric Spaces, New York, 1967.
  • [6] W. Sierpiski, Sur une courbe cantorienne qui contient une image biunivoque et continue de toute courbe donne, Comptes Rendus, 162 (1916), 629-642.
  • [7] H. Wegmann, Die HausdorfF-Dimension von kartesischen Produkten metrischer Raume, J. reine angew. Math., 246 (1971), 46-75. Department of Mathematics Harvard University Cambridge Massachusetts 01238 USA