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Choquet–Kendall–Matheron theorems for non-Hausdorff spaces

Published online by Cambridge University Press:  28 January 2011

JEAN GOUBAULT-LARRECQ
Affiliation:
LSV, ENS Cachan, CNRS, INRIA Saclay, 61 avenue du Président-Wilson, 94230 Cachan, France Email: goubault@lsv.ens-cachan.fr
KLAUS KEIMEL
Affiliation:
Fachbereich Mathematik, Technische Universität, 64289 Darmstadt, Germany Email: keimel@mathematik.tu-darmstadt.de

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.

Type
Paper
Copyright
Copyright © Cambridge University Press 2011

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