Probability measure monad on the category of ultrametric spaces

O.B. Hubal, M.M. Zarichnyi

Abstract

The set of all probability measures with compact support on an ultrametric space can be endowed with a natural ultrametric. We show that the functor of probability measures with finite supports (respectively compact supports) forms a monad in the category of ultrametric spaces (respectively complete ultrametric spaces) and nonexpanding maps. It is also proven that the G-symmetric power functor has an extension onto the Kleisli category of the probability measure monad.

Keywords

Probability measure; Ultrametric space; Monad; Kleisli category

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