  We propose the general way of study the universal estimator for the
regression problem in learning theory considered in "Universal algorithms for
learning theory Part I: piecewise constant functions" and "Universal algorithms
for learning theory Part II: piecewise constant functions" written by Binev,
P., Cohen, A., Dahmen, W., DeVore, R., Temlyakov, V. This new approch allows us
to improve results.
