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Weighted uniform densities

Rita Giuliano AntoniniGeorges Grekos — 2007

Journal de Théorie des Nombres de Bordeaux

We introduce the concept of uniform weighted density (upper and lower) of a subset A of * , 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...

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