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Positive-measure self-similar sets without interior

By M. Csörnyei, Thomas Jordan, Mark Pollicott, David Preiss and B. Solomyak

Abstract

We recall the problem posed by Peres and Solomyak in Problems on self-similar and self-affine sets; an update. Progr. Prob. 46 (2000), 95–106: can one find examples of self-similar sets with positive Lebesgue measure, but with no interior? The method in Properties of measures supported on fat Sierpinski carpets, this issue, leads to families of examples of such sets

Topics: QA
Publisher: Cambridge University Press
Year: 2006
OAI identifier: oai:wrap.warwick.ac.uk:712

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Citations

  1. (1998). Measure and dimension for some fractal families. doi
  2. (2000). Problems on self-similar and self-affine sets; an update. doi
  3. Properties of measures supported on fat Sierpinski carpets, this issue. doi
  4. (1988). The Hausdorff dimension of self-affine fractals. doi

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