On sets containing an affine copy of bounded decreasing sequences
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Publication:2007442
DOI10.1007/S00041-020-09780-4zbMATH Open1479.28009arXiv1901.06429OpenAlexW3084051035MaRDI QIDQ2007442
Publication date: 14 October 2020
Published in: The Journal of Fourier Analysis and Applications (Search for Journal in Brave)
Abstract: How small can a set be while containing many configurations? Following up on earlier work of ErdH os and Kakutani cite{MR0089886}, M'ath'e cite{MR2822418} and Molter and Yavicoli cite{Molter}, we address the question in two directions. On one hand, if a subset of the real numbers contains an affine copy of all bounded decreasing sequences, then we show that such subset must be somewhere dense. On the other hand, given a collection of convergent sequences with prescribed decay, there is a closed and nowhere dense subset of the reals that contains an affine copy of every sequence in that collection.
Full work available at URL: https://arxiv.org/abs/1901.06429
Contents, measures, outer measures, capacities (28A12) Fractals (28A80) Density, gaps, topology (11B05) Arithmetic progressions (11B25) Hausdorff and packing measures (28A78)
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