A De Finetti-type theorem for nonexchangeable finite-valued random variables

We introduce the concept of a random assignment process (roughly speaking, such a process assigns, according to some weight function, labels to the points of an arbitrary set), and we impose conditions on the weight function ensuring that a De Finetti-type theorem is satisfied. In particular, this provides a wide class of finite-valued random variables which, despite they are neither exchangeable nor identically distributed, verify a De Finetti-type theorem (i.e., they are conditionally independent).