  The problem of prediction consists in forecasting the conditional
distribution of the next outcome given the past. Assume that the source
generating the data is such that there is a stationary ergodic predictor whose
error converges to zero (in a certain sense). The question is whether there is
a universal predictor for all such sources, that is, a predictor whose error
goes to zero if any of the sources that have this property is chosen to
generate the data. This question is answered in the negative, contrasting a
number of previously established positive results concerning related but
smaller sets of processes.
