The classical representation theorem of Skorohod states that if a sequence \(\mathbf Q_n\) of countably additive probabilities on a Polish space converges in weak*-topology then, on a standard probability space, there exist \(\mathbf Q_n-\)distributed \(f_n\) which converge almost surely. In this paper the author formulates and studies this theorem for vector measures with values in \(R^d.\) An application is made to the following Monge problem: if \(|\mathbf P |\) is the variation of the vector measure \(\mathbf P, (\mathbf P, \mathbf Q)\) be a couple, and \(c\) is a cost function, a function \(\phi\) exists such that \(\phi(\mathbf P) = \mathbf Q\) and \(E_{| \mathbf P|} c(x, \phi(x)\) = inf \(\{E_{(X, Y)( \mathbf P)} (c)\), \(X(\mathbf P) = \mathbf P, Y(\mathbf P) = \mathbf Q\}\). It is shown that such a function exists for a quadratic cost.