University of Oulu

Zoltán Buczolich, Esa Järvenpää, Maarit Järvenpää, Tamás Keleti, Tuomas Pöyhtäri, Fractal percolation is unrectifiable, Advances in Mathematics, Volume 390, 2021, 107906, ISSN 0001-8708,

Fractal percolation is unrectifiable

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Author: Buczolich, Zoltán1; Järvenpää, Esa2; Järvenpää, Maarit2;
Organizations: 1Department of Analysis, ELTE Eötvös Loránd University, Pázmány Péter sétány 1/c, H-1117 Budapest, Hungary
2Department of Mathematical Sciences, P.O. Box 3000, 90014 University of Oulu, Finland
Format: article
Version: published version
Access: open
Online Access: PDF Full Text (PDF, 0.9 MB)
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Language: English
Published: Elsevier, 2021
Publish Date: 2021-10-07


We show that there exists 0 < α₀ < 1 (depending on the parameters) such that the fractal percolation is almost surely purely α-unrectifiable for all α > α₀.

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Series: Advances in mathematics
ISSN: 0001-8708
ISSN-E: 1090-2082
ISSN-L: 0001-8708
Volume: 390
Article number: 107906
DOI: 10.1016/j.aim.2021.107906
Type of Publication: A1 Journal article – refereed
Field of Science: 111 Mathematics
Copyright information: © 2021 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY license (