Nonuniqueness ing-functions

We give an example of two distinct stationary processes {Xn} and {X′n} on {0, 1} for whichP[X0=1|X−1=a−1,X−2=a−2, …]=P[X′0=1|X′−1=a−1,X′−2=a−2, …] for all {ai},i=−1, −2, …, even though these probabilities are bounded away from 0 and 1, and are continuous in {ai}.