Continuous version of the Choquet Integral Reperesentation Theorem

Details Continuous version of the Choquet Integral Reperesentation Theorem Continuous version of the Choquet Integral Reperesentation Theorem

2004-05-12

arxiv.org/abs/math/0405217v2

Studia Math. 168 (1), 2005, 15-24

Mathematics

Functional Analysis

9 pages, minor historical, editorial and bibliographical changes; version as appeared in the journal

Scientific paper

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.

Affiliated with

Also associated with

No associations

Rating

Continuous version of the Choquet Integral Reperesentation Theorem does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Continuous version of the Choquet Integral Reperesentation Theorem, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Continuous version of the Choquet Integral Reperesentation Theorem will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-536753