2015/11/18 by Ben Berckmoes, Berckmoes, Ben, Bob Lowen +1
Mathematics · #60A05 #FOS: Mathematics #Probability (math.PR) #math.PR #msc:60A05
paper · pdf · doi:10.48550/arxiv.1511.05878
8 pages
arxiv created 2015/11/18 · arxiv updated 2015/11/19
Probability metrics constitute an important tool in probability theory and statistics \citeDKS91, \citeR91, \citeZ83 as they are specific metrics on spaces of random variables which, by satisfying an extra condition, concord well with the randomness structure. But probability metrics suffer from the same instability under constructions as metrics. In \citeL15, as well as in former and related work which can be found in the references of \citeL15, a comprehensive setting was developed to deal with this. It is the purpose of this note to point out that these ideas can also be applied to probability metrics thus embedding them in a natural categorical framework, showing that certain constructions performed in the setting of probability theory are in fact categorical in nature. This allows us to deduce various separate results in the literature from a unified approach.