Probabilistic Observations and Valuations

We give a universal property for an “abstract probabilistic powerdomain” based on an analysis of observable properties of probabilistic computation. The universal property determines an abstract notion of integration satisfying the usual equational laws. In the category of topological spaces, the abstract probabilsitic powerdomain is given explicitly by the space of continuous probability valuations with weak topology. Thus our abstract notion of integration coincides with the usual integration for probability valuations. We end by discussing how our approach might adapt to provide “abstract effect spaces” for other computational effects