Currently displaying 1 – 13 of 13

Showing per page

Order by Relevance | Title | Year of publication

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...

Some generalizations of Olivier's theorem

Alain FaisantGeorges GrekosLadislav Mišík — 2016

Mathematica Bohemica

Let n = 1 a n be a convergent series of positive real numbers. L. Olivier proved that if the sequence ( a n ) is non-increasing, then lim n n a n = 0 . In the present paper: (a) We formulate and prove a necessary and sufficient condition for having lim n n a n = 0 ; 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...

Page 1

Download Results (CSV)