Probabilistic Observations and Valuations

Matthias Schröder, Alex Simpson
2006 Electronical Notes in Theoretical Computer Science  
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 expected equational properties. In the category of topological spaces, the abstract probabilsitic powerdomain is given explicitly as the space of continuous probability valuations with weak topology. It follows that our abstract notion of integration coincides with
more » ... e usual integration with respect to probability valuations. We end by discussing how our approach might adapt to provide "abstract effect spaces" for other computational effects.
doi:10.1016/j.entcs.2005.11.075 fatcat:5f2a7oafhvhshpzbrwplqjzt64