  A new negative result for nonparametric distribution estimation of binary
ergodic processes is shown. The problem of estimation of distribution with any
degree of accuracy is studied. Then it is shown that for any countable class of
estimators there is a zero-entropy binary ergodic process that is inconsistent
with the class of estimators. Our result is different from other negative
results for universal forecasting scheme of ergodic processes. We also
introduce a related result by B. Weiss.
