Probability measure monad on the category of ultrametric spaces

• Hubal, O.B. ^[1] ; Zarichnyi, M.M. ^[1]
  1. [1] Lviv National University
• Localización: Applied general topology, ISSN-e 1989-4147, ISSN 1576-9402, Vol. 9, Nº. 2, 2008, págs. 229-237
• Idioma: inglés
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• Resumen

  • 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.