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 <span class="tex">L<sub>1</sub></span> 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 <span class="tex">L<sub>1</sub></span> Density Estimation" at the Prague Stochastics 2010 Symposium. In this paper we complete his task, i.e., we translate the Cencov's chapter and insert some remarks on the related literature focusing primarily on Igor's results. We would also like to acknowledge the excellent work of Alexandre Tsybakov who translated the Devroye and Györfi book in Russian, annotated it with valuable comments and included some related references published in Russian only.
The paper is concerned with generalized (i. e. monotone and possibly non-additive) measures. A discussion concerning the classification of these measures, according to the type and amount of non-additivity, is done. It is proved that λ-additive measures appear naturally as solutions of functional equations generated by the idea of (possible) non additivity.