Farkas’ lemma in random locally convex modules and Minkowski-Weyl type results in \(L^0(\mathcal F,R^n)\). (English) Zbl 1329.46007
Summary: In this paper, we investigate the structure of a finitely generated \(L^0\)-positively homogeneous and \(L^0\)-convex cone in a random locally convex module. First, we establish a Farkas type characterization for such a kind of cone. Then, we can further give some Minkowski-Weyl type results for the specific case when the random locally convex module is the space \(L^0(\mathcal F,\mathbb{R}^n)\) of equivalence classes of \(\mathbb{R}^n\)-valued random variables.
MSC:
| 46A55 | Convex sets in topological linear spaces; Choquet theory |
| 46H25 | Normed modules and Banach modules, topological modules (if not placed in 13-XX or 16-XX) |
| 52A22 | Random convex sets and integral geometry (aspects of convex geometry) |
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