  For probability measures on a complete separable metric space, we present
sufficient conditions for the existence of a solution to the Kantorovich
transportation problem. We also obtain sufficient conditions (which sometimes
also become necessary) for the convergence, in transportation, of probability
measures when the cost function is continuous, non-decreasing and depends on
the distance. As an application, the CLT in the transportation distance is
proved for independent and some dependent stationary sequences.
