Probability measure monad on the category of ultrametric spaces

O.B. Hubal, M.M. Zarichnyi


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.


Probability measure; Ultrametric space; Monad; Kleisli category

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