The problem of convergence in law of normed sums of exchangeable random
variables is examined. First, the problem is studied w.r.t. arrays of
exchangeable random variables, and the special role played by mixtures of
products of stable laws - as limits in law of normed sums in different rows of
the array - is emphasized. Necessary and sufficient conditions for convergence
to a specific form in the above class of measures are then given. Moreover,
sufficient conditions for convergence of sums in a single row are proved.
Finally, a potentially useful variant of the formulation of the results just
summarized is briefly sketched, a more complete study of it being deferred to a
future work
