
02126075
j
02126075
AlvarezManilla, Mauricio
Jung, Achim
Keimel, Klaus
The probabilistic powerdomain for stably compact spaces.
Theor. Comput. Sci. 328, No. 3, 221244 (2004).
2004
Elsevier, Amsterdam
EN
Probabilistic powerdomain
Stably compact space
Valuation
doi:10.1016/j.tcs.2004.06.021
Summary: This paper reviews the onetoone correspondence between stably compact spaces (a topological concept covering most classes of semantic domains) and compact ordered Hausdorff spaces. The correspondence is extended to certain classes of realvalued functions on these spaces. This is the basis for transferring methods and results from functional analysis to the nonHausdorff setting. As an application of this, the Riesz Representation Theorem is used for a straightforward proof of the (known) fact that every valuation on a stably compact space extends uniquely to a Radon measure on the Borel algebra of the corresponding compact Hausdorff space. The view of valuations and measures as certain linear functionals on function spaces suggests considering a weak topology for the space of all valuations. If these are restricted to the probabilistic or subprobabilistic case, then another stably compact space is obtained. The corresponding compact ordered space can be viewed as the set of (probability or subprobability) measures together with their natural weak topology.