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The problem of convergence in law of normed sums of exchangeable randomvariables is examined. First, the problem is studied w.r.t. arrays ofexchangeable random variables, and the special role played by mixtures ofproducts of stable laws - as limits in law of normed sums in different rows ofthe array - is emphasized. Necessary and sufficient conditions for convergenceto 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 justsummarized is briefly sketched, a more complete study of it being deferred to afuture work.

Central Limit Theorem with Exchangeable Summands and Mixtures of Stable Laws as Limits