@article{alvarez04,
author = {M. Alvarez-Manilla and A. Jung and K. Keimel},
title = {The probabilistic powerdomain for stably compact spaces},
journal = {Theoretical Computer Science},
year = 2004,
volume = 328,
publisher = elsevier,
pages = 221--244,
abstract = {This paper reviews the one-to-one 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 real-valued
functions on these spaces. This is the basis for transferring
methods and results from functional analysis to the non-Hausdorff
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
sub-probabilistic case, then another stably compact space is
obtained. The corresponding compact ordered space can be viewed as
the set of (probability or sub-probability) measures together with
\emph{their} natural weak topology.}
}