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On weighted uniform density. (English) Zbl 1219.11014

T. C. Brown and A. R. Freedman [Rocky Mt. J. Math. 17, 587–596 (1987; Zbl 0632.10052)] was introduced the notion of uniform density. R. Giuliano Antonini and G. Grekos [J. Theor. Nombres Bordx. 19, 191–204, (2007; Zbl 1128.11005)] generalized this notion to weighted uniform density. In this paper the authors obtained a new limit expression of the upper and lower weighted uniform density. The set of positive integers has weighted uniform density if such limits have the same value. Including some conditions on weights, the authors give another characterizations of upper and lower uniform density, generalizing R. Giuliano Antonini and G. Grekos [loc. cit.]. Several examples are given.

MSC:

11B05 Density, gaps, topology
11K06 General theory of distribution modulo \(1\)
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