A1 Journal article (refereed)
Combinatorial proofs of two theorems of Lutz and Stull (2021)
Orponen, T. (2021). Combinatorial proofs of two theorems of Lutz and Stull. Mathematical proceedings of the Cambridge Philosophical Society, 171(3), 503-514. https://doi.org/10.1017/S0305004120000328
JYU authors or editors
Publication details
All authors or editors: Orponen, Tuomas
Journal or series: Mathematical proceedings of the Cambridge Philosophical Society
ISSN: 0305-0041
eISSN: 1469-8064
Publication year: 2021
Publication date: 15/02/2021
Volume: 171
Issue number: 3
Pages range: 503-514
Publisher: Cambridge University Press (CUP)
Publication country: United Kingdom
Publication language: English
DOI: https://doi.org/10.1017/S0305004120000328
Publication open access: Not open
Publication channel open access:
Publication is parallel published (JYX): https://jyx.jyu.fi/handle/123456789/74553
Publication is parallel published: https://arxiv.org/abs/2002.01743
Abstract
Recently, Lutz and Stull used methods from algorithmic information theory to prove two new Marstrand-type projection theorems, concerning subsets of Euclidean space which are not assumed to be Borel, or even analytic. One of the theorems states that if K⊂Rn is any set with equal Hausdorff and packing dimensions, then dimHπe(K)=min{dimHK,1} for almost everye ∈Sn−1. Here π estands for orthogonal projection to span(e). The primary purpose of this paper is to present proofs for Lutz and Stull’s projection theorems which do not refer to information theoretic concepts. Instead, they will rely on combinatorial-geometric arguments, such as discretised versions of Kaufman’s “potential theoretic” method, the pigeonhole principle, and a lemma of Katz and Tao. A secondary purpose is to generalise Lutz and Stull’s theorems: the versions in this paper apply to orthogonal projections tom-planes in Rn, for all 0
Keywords: measure theory; fractals; combinatorics
Free keywords: Hausdorff and packing measures
Contributing organizations
Ministry reporting: Yes
Reporting Year: 2021
JUFO rating: 2