  Multi-class systems having possibly both finite and infinite classes are
investigated under a natural partial exchangeability assumption. It is proved
that the conditional law of such a system, given the vector of the empirical
measures of its finite classes and directing measures of its infinite ones
(given by the de Finetti Theorem), corresponds to sampling independently from
each class, without replacement from the finite classes and i.i.d. from the
directing measure for the infinite ones. The equivalence between the
convergence of multi-exchangeable systems with fixed class sizes and the
convergence of the corresponding vectors of measures is then established.
