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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
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Official URL: https://doi.org/10.1090/proc/14621
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 | ||||||
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| Subjects: | Q Science > QA Mathematics | ||||||
| Divisions: | Faculty of 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: |
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| Volume: | 147 | ||||||
| Page Range: | pp. 4891-4899 | ||||||
| DOI: | 10.1090/proc/14621 | ||||||
| Status: | Peer Reviewed | ||||||
| Publication Status: | Published | ||||||
| Publisher Statement: | 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 | ||||||
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