Ein Masstheoretisches Marginalproblem

Let ((X_i, K_i, _i) iI) be a family of normed measure spaces. We study the extremal points of the convex set F of normed measures on the product of ((X_i, K_i): iI) with the marginal measures _i. We give a construction principle for extremal points. If _i is the Lebesgue measure on 0, 1] and I is countable, we prove by using this principle that the set of extremal points of F is weakly dense in F. Finally we give a necessary and some sufficient conditions for extremal points in the case that I={1,2} and _i is the Lebesgue measure on 0,1] for i=1,2.