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An infinitely generated self-similar set with positive Lebesgue measure and empty interior

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Baker, Simon and Sidorov, Nikita (2019) An infinitely generated self-similar set with positive Lebesgue measure and empty interior. Proceedings of the American Mathematical Society, 147 . pp. 4891-4899. doi:10.1090/proc/14621 ISSN 0002-9939.

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Official URL: https://doi.org/10.1090/proc/14621

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Abstract

In [5] Peres and Solomyak asked the question: Do there exist self-similar sets with positive Lebesgue measure and empty interior? This question was answered in the affirmative by Cs¨ornyei et al in [1]. 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.

Item Type: Journal Article
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Science, Engineering and Medicine > Science > Mathematics
Journal or Publication Title: Proceedings of the American Mathematical Society
Publisher: American Mathematical Society
ISSN: 0002-9939
Official Date: 20 March 2019
Dates:
DateEvent
20 March 2019Available
12 March 2019Accepted
Volume: 147
Page Range: pp. 4891-4899
DOI: 10.1090/proc/14621
Status: Peer Reviewed
Publication Status: Published
Reuse Statement (publisher, data, author rights): First published in Proceedings of the American Mathematical Society in 147, 4891-4899, 2019 published by the American Mathematical Society.
Access rights to Published version: Restricted or Subscription Access
Date of first compliant deposit: 12 April 2019
Date of first compliant Open Access: 11 October 2019
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