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Positive-measure self-similar sets without interior

Published online by Cambridge University Press:  01 June 2006

M. CSÖRNYEI ,
T. JORDAN ,
M. POLLICOTT ,
D. PREISS  and
B. SOLOMYAK
M. CSÖRNYEI
Affiliation:
Department of Mathematics, University College London, Gower Street, London WC1E 6BT, UK (e-mail: m.csornyei@ucl.ac.uk, dp@ucl.ac.uk)
T. JORDAN
Affiliation:
Department of Mathematics, Warwick University, Coventry CV4 7AL, UK (e-mail: tjordan@maths.warwick.ac.uk, mpollic@maths.warwick.ac.uk)
M. POLLICOTT
Affiliation:
Department of Mathematics, Warwick University, Coventry CV4 7AL, UK (e-mail: tjordan@maths.warwick.ac.uk, mpollic@maths.warwick.ac.uk)
D. PREISS
Affiliation:
Department of Mathematics, University College London, Gower Street, London WC1E 6BT, UK (e-mail: m.csornyei@ucl.ac.uk, dp@ucl.ac.uk)
B. SOLOMYAK
Affiliation:
Department of Mathematics, University of Washington, Box 354350, Seattle, WA 98195-4350, USA (e-mail: solomyak@math.washington.edu)
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Abstract

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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.

Information

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 26 , Issue 3 , June 2006 , pp. 755 - 758
Copyright
2006 Cambridge University Press