Monge problem for \(n\) probabilities (Q1600170)

The author extends a result of \textit{W. Gangbo} and \textit{A. Świȩch} [Commun. Pure Appl. Math. 51, No. 1, 23-45 (1998; Zbl 0889.49030)] on the existence of optimal Monge functions for coupling functions \(c(x)= (\sum x_i)^2\) to the case where \(c(x)\) is of the form \(h(\sum x_i)\), \(h\) convex, \(h(0)= 0\), and furthermore, to the more general case of Köthe spaces. The method of proof is similar to a related proof of the Gangbo-Świȩch result by the reviewer and \textit{Uckelmann} (2002).