Conditions on the distribution of a process { Xn, n E I} are given under which the invariant, tail and exchangeable a-fields coincide; the index set I is either the positive integers or all the integers. The results proven here correct similar statements given in [3]. 1. Let {Xn, n E I) be a sequence of real-valued r.v.'s on the probability space (Vi , 'R10 P), let 4, C, and & be the invariant, tail, and exchangeable a-fields (see [3] for definitions and terminology), and consider the case where I is the set of positive integers J. It is well known (see [2, p. 39; or 4]) that without reference to the probability P, the following strict inclusions always hold: (1) c c S. Hence, for any probability P: (2) 4 C JC i(P). Looking at (1) and (2) one can see that Theorem 1 in [3] is erroneous. The inaccuracies in [3] stem from not considering separately the case where I is J, the positive integers, and the case where I is Z, the integers. 2. Z setup. In this case one can define 4 and S as before mutatis mutandis (now T is onto as well as 1-1, and the permutations move around a finite number of possibly negative and positive coordinates); there are, however, several a-fields that could merit being called "tail a-field". (For a discussion of these a-fields, and many more things related to this note and to [1], see [4].) We will be satisfied here considering T to be , a(Xi i n), where a(Xi, i E I) denotes the a-field generated by the variables Xi, i E I. In this setup it is known that