Abstract
In this section, we assume S to be a compact and metric space.
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Notes and references
Example III:1 is due to B. Fuglede, Capacity as a sublinear functional generalizing an integral. Der Kongelige Danske Videnskabernes Selskab. Matematisk-fysiske Meddelelser. 38.7 (1971).
The existence of a Gδ-set A with properties 1) and 2) in Example III:3 was proved by Roy O. Davies, A non-Prokhorov space, Bull. London Math. Soc. 3 (1971), 341–342.
The use of A in this context was observed by C. Dellacherie, Ensembles analytiques, capacités, mesures de Hausdorff. Springer LNM. 295, 1972. pg. 106 Ex. 4.
Theorem III:1 is a variant of a theorem due to Choquet. See the references in Section II.
Representation of strongly subadditive capacities by measures has been studied by Bernd Anger, Representation of capacities. Math. Ann. 229 (1977), 245–258.
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© 1988 Springer Fachmedien Wiesbaden
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Cegrell, U. (1988). Outer Regularity. In: Capacities in Complex Analysis. Aspects of Mathematics / Aspekte der Mathematik, vol E 14. Vieweg+Teubner Verlag, Wiesbaden. https://doi.org/10.1007/978-3-663-14203-4_3
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DOI: https://doi.org/10.1007/978-3-663-14203-4_3
Publisher Name: Vieweg+Teubner Verlag, Wiesbaden
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