Removing of an infinite subset of an additive basis. (En enlevant d'une base additive une partie infinie.)
Suites d'entiers de densités données
Densités asymptotiques de sous-suites.
Extremal problems about additive bases
Densities in disjoint unions
Suites équivalentes
Densités, moyennes et ensemble représentatif : unification du cas discret et du cas continu
Propriétés extrémales de bases additives
Weighted uniform densities
We introduce the concept of uniform weighted density (upper and lower) of a subset of , with respect to a given sequence of weights . 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...
Regular sets and conditional density: an extension of Benford's law
We give an extension of Benford's law (first digit problem) by using the concept of conditional density, introduced by Fuchs and Letta. The main tool is the notion of regular subset of integers.
A note on uniform or Banach density
In this note we present and comment three equivalent definitions of the so called or density of a set of positive integers.
Some generalizations of Olivier's theorem
Let be a convergent series of positive real numbers. L. Olivier proved that if the sequence is non-increasing, then . In the present paper: (a) We formulate and prove a necessary and sufficient condition for having ; Olivier’s theorem is a consequence of our Theorem . (b) We prove properties analogous to Olivier’s property when the usual convergence is replaced by the -convergence, that is a convergence according to an ideal of subsets of . Again, Olivier’s theorem is a consequence of...
On weighted densities
The continuity of densities given by the weight functions , , with respect to the parameter is investigated.
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