  We proposed a learning algorithm for nonparametric estimation and on-line
prediction for general stationary ergodic sources. We prepare histograms each
of which estimates the probability as a finite distribution, and mixture them
with weights to construct an estimator. The whole analysis is based on measure
theory. The estimator works whether the source is discrete or continuous. If it
is stationary ergodic, then the measure theoretically given Kullback-Leibler
information divided by the sequence length $n$ converges to zero as $n$ goes to
infinity. In particular, for continuous sources, the method does not require
existence of a probability density function.
