Farkas' lemma in random locally convex modules and Minkowski-Weyl type results in L0(F,Rn)

In this paper, we investigate the structure of a finitely generated L0-positively homogeneous and L0-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 L0(F,Rn) of equivalence classes of Rn-valued random variables.