Probability measure monad on the category of ultrametric spaces

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