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

Research output: Contribution to journal › Article › peer-review

## Standard

**An infinitely generated self-similar set with positive Lebesgue measure and empty interior.** / Baker, Simon; Sidorov, Nikita.

Research output: Contribution to journal › Article › peer-review

## Harvard

*Proceedings of the American Mathematical Society*, vol. 147, pp. 4891-4899. https://doi.org/10.1090/proc/14621

## APA

*Proceedings of the American Mathematical Society*,

*147*, 4891-4899. https://doi.org/10.1090/proc/14621

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## Bibtex

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## RIS

TY - JOUR

T1 - An infinitely generated self-similar set with positive Lebesgue measure and empty interior

AU - Baker, Simon

AU - Sidorov, Nikita

N1 - First published in Proceedings of the American Mathematical Society in vol.147, 2019, published by the American Mathematical Society

PY - 2019/3/20

Y1 - 2019/3/20

N2 - 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.

AB - 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.

U2 - 10.1090/proc/14621

DO - 10.1090/proc/14621

M3 - Article

VL - 147

SP - 4891

EP - 4899

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

SN - 0002-9939

ER -