A colleague here at U.N.B. has provided a counter example for me. So the conjecture (that the existance of the ``product limit'' is implied by the existance of the limits involving the first three powers) is false. If anyone is interested in the details, they should contact me off-list. My apologies for confusing everyone with my initial mis-statement of the problem. cheers, Rolf Turner rolf at math.unb.ca