Large subsets of Euclidean space avoiding infinite arithmetic progressions
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Publication:6039983
DOI10.1090/PROC/16404zbMath1519.28002arXiv2205.04786OpenAlexW4318774077MaRDI QIDQ6039983
Yuveshen Mooroogen, Unnamed Author, Unnamed Author
Publication date: 24 May 2023
Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)
Abstract: It is known that if a subset of $mathbb{R}$ has positive Lebesgue measure, then it contains arbitrarily long finite arithmetic progressions. We prove that this result does not extend to infinite arithmetic progressions in the following sense: for each $lambda$ in $[0,1)$, we construct a subset of $mathbb{R}$ that intersects every interval of unit length in a set of measure at least $lambda$, but that does not contain any infinite arithmetic progression.
Full work available at URL: https://arxiv.org/abs/2205.04786
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Related Items (2)
Large sets avoiding Infinite arithmetic / geometric progressions ⋮ Large sets containing no copies of a given infinite sequence
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