On $\ast$-measure monads on the category of ultrametric spaces

Abstract

The functor of $\ast$-measures of compact support on the category of ultrametric spaces and non-expanding maps is introduced in the previous publication of the authors. In the present note, we prove that this functor determines a monad on this category. The monad structure allows us to define the tensor product of $\ast$-measures. We consider some applications of this notion to equilibrium theory.