Csörnyei, M., Jordan, Thomas, Pollicott, Mark, Preiss, David and Solomyak, B.. (2006) Positive-measure self-similar sets without interior. Ergodic Theory and Dynamical Systems, Vol.26 (No.3). pp. 755-758. ISSN 0143-3857

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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.

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of Science > Mathematics
Library of Congress Subject Headings (LCSH):	Measure theory, Integrals, Generalized, Lebesgue integral
Journal or Publication Title:	Ergodic Theory and Dynamical Systems
Publisher:	Cambridge University Press
ISSN:	0143-3857
Date:	June 2006
Volume:	Vol.26
Number:	No.3
Page Range:	pp. 755-758
Identification Number:	10.1017/S0143385705000702
Status:	Peer Reviewed
Access rights to Published version:	Open Access
References:	[1] T. Jordan and M. Pollicott. Properties of measures supported on fat Sierpinski carpets, this issue. [2] Y. Peres and B. Solomyak. Problems on self-similar and self-affine sets; an update. Progr. Prob. 46 (2000), 95–106. [3] K. Falconer. The Hausdorff dimension of self-affine fractals. Math. Proc. Cambridge Philos. Soc. 103 (1988), 339–350. [4] B. Solomyak. Measure and dimension for some fractal families. Math. Proc. Cambridge Philos. Soc. 124 (1998), 531–546.
URI:	http://wrap.warwick.ac.uk/id/eprint/712

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