Article
Comparison Between Lower and Upper Α−densities and Lower and Upper Α−analytic Densities
Authors
and
Abstract
Let α be a real number, with α ≥ −1. We prove a general in- equality between the upper (resp. lower) α−analytic density and the upper (resp. lower) α−density of a subset A of N∗ (Proposition 2.1). Moreover, we prove by an example that the upper and the lower α–densities and the lower and upper α–analytic densities of A do not coincide in general (i.e., the inequalities proved in (2.1) may be strict). On the other hand, we identify a class of subsets of N∗ for which these values do coincide in the case α > −1.
Keywords
α−density, α−analytic density, logarithmic density, analytic density, tauberian.
Citation
Antonini, R. G. & Grekos, G. (2008). Comparison between lower and upper α−densities and lower and upper α−analytic densities. Uniform Distribution Theory, 3(2), 21–35.
R. G. Antonini and G. Grekos, “Comparison between lower and upper α−densities and lower and upper α−analytic densities,” Uniform Distribution Theory, vol. 3, no. 2, pp. 21–35, 2008.
Antonini RG, Grekos G. Comparison between lower and upper α−densities and lower and upper α−analytic densities. Uniform Distribution Theory. 2008;3(2):21–35.
Antonini, R. G. and Grekos, G. (2008), ‘Comparison between lower and upper α−densities and lower and upper α−analytic densities’, Uniform Distribution Theory, 3(2), pp. 21–35.
Antonini, Rita Giuliano, and Georges Grekos. “Comparison Between Lower and Upper Α−densities and Lower and Upper Α−analytic Densities.” Uniform Distribution Theory, vol. 3, no. 2, 2008, pp. 21–35.
Antonini, Rita Giuliano, and Georges Grekos. “Comparison Between Lower and Upper Α−densities and Lower and Upper Α−analytic Densities.” Uniform Distribution Theory 3, no. 2 (2008): 21–35.
Export citation
Published by: Engineering Journals
