Admissible representations for probability measures
Matthias Schröder · Mathematical logic quarterly · 2007
Abstract In a recent paper, probabilistic processes are used to generate Borel probability measures on topological spacesXthat 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 onX. 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)