Representing Probability Measures using Probabilistic Processes

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. Key words: Borel measures, probabilistic processes, Type-2 Theory of Effectivity

• Type: Conference
• Year: 2005
• Where: CCA
• Authors: Matthias Schröder, Alex K. Simpson
• Keywords: Borel Probability Measures, CCA 2005, Probabilistic, Probabilistic Processes