Continuous version of the Choquet Integral Reperesentation Theorem
| dc.creator | Puchała, Piotr | |
| dc.date | 2004-05-12 | |
| dc.date | 2005-04-05 | |
| dc.date.accessioned | 2026-07-07T05:08:10Z | |
| dc.date.available | 2026-07-07T05:08:10Z | |
| dc.description | The Choquet - Bishop - de Leeuw theorem states that each element of a compact convex subset of a locally convex topological Hausdorff space is a barycenter of a probability measure supported by the set of extreme points of that set. By the Edgar - Mankiewicz result this remains true for nonempty closed bounded and convex set provided it has Radon - Nikodym property. In the paper it is shown, that Choquet - type theorem holds also for "moving" sets: they are values of a certain multifunction. Namely, the existence of a suitable weak* continuous family of probability measures "almost representing" points of such sets is proven. Both compact and noncompact cases are considered. The continuous versions of the Krein - Milman theorem are obtained as corollaries. | |
| dc.description | 9 pages, minor historical, editorial and bibliographical changes; version as appeared in the journal | |
| dc.identifier | https://arxiv.org/abs/math/0405217 | |
| dc.identifier | http://arxiv.org/abs/math/0405217 | |
| dc.identifier | Studia Math. 168 (1), 2005, 15-24 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/71152 | |
| dc.subject | Functional Analysis | |
| dc.subject | 54C60; 54C65; 46A55; 46B22 | |
| dc.title | Continuous version of the Choquet Integral Reperesentation Theorem | |
| dc.type | text |