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Journal of Convex Analysis 21 (2014), No. 4, 1141--1164
Copyright Heldermann Verlag 2014

Choquet Theory for Vector-Valued Functions on a Locally Compact Space

Walter Roth
Dept. of Mathematics, Universiti Brunei Darussalam,, Gadong BE1410, Brunei Darussalam

We consider spaces of continuous vector-valued functions on a locally compact Hausdorff space X, endowed with suitable locally convex topologies. Using a family of sets of such functions an order on the dual of the function space is defined. This order yields minimal elements which as in classical Choquet theory can be characterized in terms of a subset (Choquet boundary) of X, thus providing information about the support of their representation measures.

Keywords: Vector-valued functions, integral representation.

MSC: 46A22, 46A03, 46A20

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