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Admissible representations for probability measures
Author(s) -
Schröder Matthias
Publication year - 2007
Publication title -
mathematical logic quarterly
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.473
H-Index - 28
eISSN - 1521-3870
pISSN - 0942-5616
DOI - 10.1002/malq.200710010
Subject(s) - mathematics , probability measure , probabilistic logic , representation (politics) , polish space , borel measure , borel set , unit interval , measure (data warehouse) , discrete mathematics , borel hierarchy , topological space , pure mathematics , topology (electrical circuits) , combinatorics , mathematical analysis , statistics , computer science , separable space , database , politics , political science , law
In a recent paper, probabilistic processes are used to generate Borel probability measures on topological spaces X that are equipped with a representation in the sense of type‐2 theory of effectivity. This gives rise to a natural representation of the set of Borel probability measures on X . We compare this representation to a canonically constructed representation which encodes a Borel probability measure as a lower semicontinuous function from the open sets to the unit interval. We show that this canonical representation is admissible with respect to the weak topology on Borel probability measures. Moreover, we prove that for countably‐based topological spaces the representation via probabilistic processes is equivalent to the canonical representation and thus admissible with respect to the weak topology. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)