  We construct a stationary Markov process with trivial tail sigma-field and a
nondegenerate observation process such that the corresponding nonlinear
filtering process is not uniquely ergodic. This settles in the negative a
conjecture of the author in the ergodic theory of nonlinear filters arising
from an erroneous proof in the classic paper of H. Kunita (1971), wherein an
exchange of intersection and supremum of sigma-fields is taken for granted.
