An infinitely generated self-similar set with positive Lebesgue measure and empty interior
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Colleges, School and Institutes
In [Problems on self-similar sets and self-affine sets: An update, Birkhäuser, Basel, 2000] Peres and Solomyak ask the question: Do there exist self-similar sets with positive Lebesgue measure and empty interior? This question was answered in the affirmative by Csörnyei et al. in 2006. The authors of that paper gave a parameterised family of iterated function systems for which almost all of the corresponding self-similar sets satisfied the required properties. They did not however provide an explicit example. Motivated by a desire to construct an explicit example, we provide an explicit construction of an infinitely generated self-similar set with positive Lebesgue measure and empty interior.
First published in Proceedings of the American Mathematical Society in vol.147, 2019, published by the American Mathematical Society
|Journal||Proceedings of the American Mathematical Society|
|Publication status||Published - 20 Mar 2019|