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arXiv · 1806.00634

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

Simon Baker·Nikita Sidorov
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Abstract

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\"{o}rnyei et al. They gave a parameterised family of iterated function systems for which almost all of the corresponding self-similar sets satisfied the required properties. They do not however provide an explicit example. Motivated by a desire to construct an explicit example, we in this paper provide an explicit construction of an infinitely generated self-similar set with positive Lebesgue measure and empty interior.

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Simon Baker, Nikita Sidorov. 2018-06-02. An infinitely generated self-similar set with positive Lebesgue measure and empty interior. https://doi.org/10.1090/proc/14621

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