The first comprehensive account of the theory of mass transportation problems and its applications. In Volume I, the authors systematically develop the theory with emphasis on the Monge-Kantorovich mass transportation and the Kantorovich-Rubinstein mass transshipment problems. They then discuss a variety of different approaches towards solving these problems and exploit the rich interrelations to several mathematical sciences - from functional analysis to probability theory and mathematical economics. The second volume is devoted to applications of the above problems to topics in applied...

1.1 Mass Transportation Problems in Probability Theory This chapter provides a basic introduction to mass transportation pr- lems (MTPs). We introduce some of the methods used in studying MTPs: dualrepresentations, explicitsolutions, topologicalproperties.Weshallalso discuss some applications of MTPs. The following measure-theoretic problems are well-known continuous casesofMKPs(see, forexample, Dudley(1976), LevinandMilyutin(1979), R] uschendorf (1979, 1981), Kemperman (1983), Kellerer (1984), Rachev (1984b, 1991c) and the references therein). TheMonge...