A REPRESENTATION OF THE KANTOROVICH-FUNCTIONAL

This paper establishes the representation of the generalized N-dimensi onal Wasserstein distance (Kantorovich-Functional) W-c(P-1,..., P-N) : =inf {integral(SN) c(x(1),..., x(N)) d mu(x(1),..., x(N)):pi(i) mu=P-i , i=1,..., N} in the form of W-c(P-1,..., P-N) = sup{Sigma(i=1)(N) int egral(S)f(i)dP(i)}. The conditions we impose on P-i, c and f(i) enable us to follow those classical lines of arguments which lead to the Kan torovich-Rubinstein Theorem: By elementary methods we show how the res ult for an arbitrary metric space (S, d) can be derived from the case of finite S. We also apply this result and the techniques of its proof in order to obtain a fairly simple proof of Strassen's Theorem.