A continuous analogue of Erdős' \(k\)-Sperner theorem
type: Item
instance of: scholarly article
title: A continuous analogue of Erdős' \(k\)-Sperner theorem
zbMATH Open document ID: 1436.28004
author: Themis Mitsis
author: Christos Pelekis
author: Václav Vlasák
published in: Journal of Mathematical Analysis and Applications
publication date: 2020-01-20T00:00:00Z
full work available at URL: https://arxiv.org/abs/1904.09625
review text: The authors show that the \(1\)-dimensional Hausdorff measure of a chain in the unit \(n\)-cube is at most \(n\), and that the bound is sharp. Then they obtain an upper bound for a Lebesgue measure maximization problem with constrains involving such chains, as a continuous counterpart to a theorem of Erdős regarding \(k\)-Sperner families of finite sets.
Mathematics Subject Classification ID: 28A78
Mathematics Subject Classification ID: 05D05
zbMATH DE Number: 7153846
zbMATH Keywords: chains
zbMATH Keywords: \(k\)-Sperner families
zbMATH Keywords: Hausdorff measure
zbMATH Keywords: Lebesgue measure
reviewed by: George Stoica
MaRDI profile type: Publication
OpenAlex ID: W2993888737
arXiv ID: 1904.09625
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DOI: 10.1016/J.JMAA.2019.123754
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