Some remarques on permutations which preserves the weighted density

Abstract

In this paper we study the conditions (1),(2) and (3) for the per- mutations which preserves the weighted density. These conditions are motivated by the conditions of Levy group, originated in [LEV], and studied in [OB]. In the second part we prove that under some con- ditions for the sequence of weights, for instance for the logarithmic density, the rst two conditions can be launched.