Farkas’ lemma in random locally convex modules and Minkowski–Weyl type results in

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 ( F , R n ) of equivalence classes of R n -valued random variables.