N. N. Cencov wrote a commentary chapter included in the Appendix of the Russian translation of the Devroye and Györfi book [15] collecting some arguments supporting the $L_1$ view of density estimation. The Cencov’s work is available in Russian only and it hasn’t been translated, so late Igor Vajda decided to translate the Cencov’s paper and to add some remarks on the occasion of organizing the session “25 Years of the $L_1$ Density Estimation” at the Prague Stochastics 2010 Symposium. In this paper we...