  This work provides an online learning rule that is universally consistent
under processes on (X,Y) pairs, under conditions only on the X process. As a
special case, the conditions admit all processes on (X,Y) such that the process
on X is stationary. This generalizes past results which required stationarity
for the joint process on (X,Y), and additionally required this process to be
ergodic. In particular, this means that ergodicity is superfluous for the
purpose of universally consistent online learning.
