On exponential densities and limit ratios of subsets of N
Abstract
Given α,β,γ∈[0,1] with α≤β, we prove that there exists a subset of N such that its lower and upper exponential densities and its lower and upper limit ratios are equal to α, β, γ and 1, respectively. This result provides an affirmative answer to an open problem posed by Grekos et al. (Unif Distrib Theory 6:117–130, 2011).
Citation
Li , J & Olsen , L 2020 , ' On exponential densities and limit ratios of subsets of N ' , Mediterranean Journal of Mathematics , vol. 17 , 122 . https://doi.org/10.1007/s00009-020-01559-7
Publication
Mediterranean Journal of Mathematics
Status
Peer reviewed
ISSN
1660-5446Type
Journal article
Rights
Copyright © The Author(s) 2020. Open Access. This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
Description
Funding: National Natural Science Foundation of China (11671189,11971109).Collections
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