An infinitely generated self-similar set with positive Lebesgue measure and empty interior
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- by Simon Baker and Nikita Sidorov PDF
- Proc. Amer. Math. Soc. 147 (2019), 4891-4899 Request permission
Abstract:
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.References
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Additional Information
- Simon Baker
- Affiliation: Mathematics Institute, University of Warwick, Coventry, CV4 7AL, United Kingdom
- MR Author ID: 1001612
- ORCID: 0000-0002-0716-6236
- Email: simonbaker412@gmail.com
- Nikita Sidorov
- Affiliation: School of Mathematics, The University of Manchester, Oxford Road, Manchester M13 9PL, United Kingdom
- Email: sidorov@manchester.ac.uk
- Received by editor(s): June 2, 2018
- Received by editor(s) in revised form: February 20, 2019
- Published electronically: May 17, 2019
- Communicated by: Jeremy Tyson
- © Copyright 2019 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 147 (2019), 4891-4899
- MSC (2010): Primary 28A80, 37C45
- DOI: https://doi.org/10.1090/proc/14621
- MathSciNet review: 4011521