Ergodic Theory and Dynamical Systems



Positive-measure self-similar sets without interior


M. CSÖRNYEI a1, T. JORDAN a2, M. POLLICOTT a2, D. PREISS a1 and B. SOLOMYAK a3
a1 Department of Mathematics, University College London, Gower Street, London WC1E 6BT, UK (e-mail: m.csornyei@ucl.ac.uk, dp@ucl.ac.uk)
a2 Department of Mathematics, Warwick University, Coventry CV4 7AL, UK (e-mail: tjordan@maths.warwick.ac.uk, mpollic@maths.warwick.ac.uk)
a3 Department of Mathematics, University of Washington, Box 354350, Seattle, WA 98195-4350, USA (e-mail: solomyak@math.washington.edu)

Article author query
csornyei m   [Google Scholar] 
jordan t   [Google Scholar] 
pollicott m   [Google Scholar] 
preiss d   [Google Scholar] 
solomyak b   [Google Scholar] 
 

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.

(Received June 23 2004)
(Revised November 29 2004)