Representing Probability Measures using Probabilistic Processes

Matthias Schröder , Alexander Simpson

Research output: Contribution to journalArticlepeer-review

Abstract / Description of output

In the Type-2 Theory of Effectivity, one considers representations of topological spaces in which infinite words are used as "names" for the elements they represent. Given such a representation, we show that probabilistic processes on infinite words, under which each successive symbol is determined by a finite probabilistic choice, generate Borel probability measures on the represented space. Conversely, for several well-behaved types of space, every Borel probability measure is represented by a corresponding probabilistic process. Accordingly, we consider probabilistic processes as providing "probabilistic names" for Borel probability measures. We show that integration is computable with respect to the induced representation of measures.
Original languageEnglish
Pages (from-to)768-788
Number of pages21
JournalJournal of Complexity
Issue number6
Publication statusPublished - 2006


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