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Capacities on non-Hausdorff spaces. (English) Zbl 0883.28002
Vervaat, W. (ed.) et al., Probability and lattices. Amsterdam: Centrum voor Wiskunde en Informatica (CWI). CWI Tracts. 110, 133-150 (1997).
Introducing capacities as increasing outer continuous functions $$c$$ on the compact subsets of a topological space being not necessarily Hausdorff such that $$c(\emptyset)= 0$$, the authors solve the problem for $$c$$ to be the restriction of some Radon measure and to have an extension to a Choquet capacity in connection with a broad class of non-Hausdorff spaces. Furthermore, the domain of capacities is topologized such that capacities might be viewed as semicontinuous functions. In particular, conditions might be given under which capacities are continuous lattices.
For the entire collection see [Zbl 0865.00051].

##### MSC:
 28A12 Contents, measures, outer measures, capacities 06B35 Continuous lattices and posets, applications 28C15 Set functions and measures on topological spaces (regularity of measures, etc.) 54D45 Local compactness, $$\sigma$$-compactness