Choquet-kendall-matheron theorems for non-hausdorff spaces

Authors:
Jean Goubault-larrecq;Klaus Keimel
Affiliations:
Lsv, ens cachan, cnrs, inria saclay, 61 avenue du président-wilson, 94230 cachan, france email: goubault@lsv.ens-cachan.fr;Fachbereich mathematik, technische universität, 64289 darmstadt, germany email: keimel@mathematik.tu-darmstadt.de
Venue:
Mathematical Structures in Computer Science
Year:
2011

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Abstract

We establish Choquet-Kendall-Matheron theorems on non-Hausdorff topological spaces. This typical result of random set theory is profitably recast in purely topological terms using intuitions and tools from domain theory. We obtain three variants of the theorem, each one characterising distributions, in the form of continuous valuations, over relevant powerdomains of demonic, angelic and erratic non-determinism, respectively.