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
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