Note on universal algorithms for learning theory

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.