Copulae of probability measures on product spaces

It has been proved (Sklar, 1959, Publ. Inst. Statist. Univ. Paris 8 229-231) that any multivariate distribution function depends on its arguments only through its marginal distributions. An analogous result will be proved in the general framework of probability measures on (Polish) product spaces. Many properties, holding for distribution functions, still hold in the more general situation. Some results related to convergence in probability will be examined.