ABSTRACT. Let \alpha be a real number, with \alpha>-1. We prove a general in- equality between the upper (resp. lower) \alpha-analytic density and the upper (resp. lower) \alpha-density of a subset A of N^* (Proposition 2.1). Moreover, we prove by an example that the upper and the lower \alpha-densities and the lower and upper \alpha-analytic densities of A do not coincide in general (i.e., the inequalities proved in (2.1) may be strict). On the other hand, we identify a class of subsets of N^* for which these values do coincide in the case \alpha > -1

Comparison between lower and upper a-densities and lower and upper a-analytic densities

GIULIANO, RITA;
2008-01-01

Abstract

ABSTRACT. Let \alpha be a real number, with \alpha>-1. We prove a general in- equality between the upper (resp. lower) \alpha-analytic density and the upper (resp. lower) \alpha-density of a subset A of N^* (Proposition 2.1). Moreover, we prove by an example that the upper and the lower \alpha-densities and the lower and upper \alpha-analytic densities of A do not coincide in general (i.e., the inequalities proved in (2.1) may be strict). On the other hand, we identify a class of subsets of N^* for which these values do coincide in the case \alpha > -1
2008
Giuliano, Rita; Grekos, G.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11568/122515
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