Choquet–Kendall–Matheron theorems for non-Hausdorff spaces

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 characterizing distributions, in the form of continuous valuations, over relevant powerdomains of demonic, resp. angelic, resp. erratic non-determinism.

De Groot duality and models of choice: angels, demons and nature

“…In fact, we do not require stable compactness to establish the existence of the one-to-one mapping ν → ν * : we show in Goubault-Larrecq and Keimel (2010), that core-compactness is the only required property for X in this respect. Duality, however, does require stable compactness.…”

Core-compactness of Smyth powerspaces

“…This research was partially supported by Labex DigiCosme (project ANR-11-LABEX0045-DIGICOSME) operated by ANR as part of the program "Investissement d'Avenir" Idex Paris-Saclay (ANR-11-IDEX-0003-02). We would also like to thank Jean Goubault-Larrecq for helpful discussions and pointing us to the result [5, Lemma 4.2]. The second author would like to thank Prof. Qingguo Li for hosting him as a visiting scholar at Hunan University from May to July 2019.…”

Static Analysis of Programs with Imprecise Probabilistic Inputs

“…The domain theoretic foundations of imprecise probabilities were studied by several authors, among which one of the authors of this paper [24,23,26,25]. In particular, the convex powerdomains of spaces of measures on X was studied by Mislove [31], by Tix et al [39,40], and by Morgan and McIver [30].…”