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Rita Giuliano Antonini;
Georges GrekosWeighted uniform densitiesJournal 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.
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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