Canonical row-column-exchangeable arrays

Consider a standard row-column-exchangeable array X = (Xij : i,j >= 1), i.e., Xij = f(a, [xi]i, [eta]j, [lambda]ij) is a function of i.i.d. random variables. It is shown that there is a canonical version of X, X', such that X', and [alpha]', [xi]'1, [xi]'2,..., [eta]'1, [eta]'2,..., are conditionally independent given [intersection]n >= 1 [sigma](X'ij : max(i,j) >= n). This result is quite a bit simpler to prove than the analogous result for the original array X, which is due to Aldous.