On exponential densities and limit ratios of subsets of N
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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).
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
Mediterranean Journal of Mathematics
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DescriptionFunding: National Natural Science Foundation of China (11671189,11971109).
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