Central Limit Theorems for Interchangeable Processes

Let X n (n = 1, 2, …) be a stochastic process. The random variables comprising it or the process itself will be said to be interchangeable if, for any choice of distinct positive integers i 1, i 2, H 3 …, i k, the joint distribution of depends merely on k and is independent of the integers i 1, i 2, …, i k. It was shown by De Finetti (3) that the probability measure for any interchangeable process is a mixture of probability measures of processes each consisting of independent and identically distributed random variables.