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Rita Giuliano Antonini; Georges Grekos
Weighted uniform densities
Journal de théorie des nombres de Bordeaux, 19 no. 1 (2007), p. 191-204, doi: 10.5802/jtnb.581
Article PDF | Reviews MR 2332061 | Zbl 1128.11005
Keywords: weighted uniform density, uniform density, weighted density, $\alpha$–density.

Résumé - Abstract

We introduce the concept of uniform weighted density (upper and lower) of a subset $A$ of ${\mathbb{N}}^*$, with respect to a given sequence of weights $(a_n)$. This concept generalizes the classical notion of uniform density (for which the weights are all equal to 1). We also prove a theorem of comparison between two weighted densities (having different sequences of weights) and a theorem of comparison between a weighted uniform density and a weighted density in the classical sense. As a consequence, new bounds for the set of (classical) $\alpha$–densities of $A$ are obtained.

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