On spaces of *-measures on ultrametric spaces

Abstract

The notion of * -measure on a compact Hausdorff space is introduced and investigated in a previous publication of the first named author. In the present note we consider the set of all * -measures of compact support on an ultrametric space. An ultrametrization of this set is provided, which determines a functor in the category of ultrametric spaces and non-expanding maps. We prove that this functor is locally non-expanding and preserves the class of complete ultrametric spaces.