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Theoretical Computer Science - Special issue on computability and complexity in analysis
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Theoretical Computer Science
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Electronic Notes in Theoretical Computer Science (ENTCS)
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Electronic Notes in Theoretical Computer Science (ENTCS)
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Theoretical Computer Science
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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.