The paper deals with upper and lower bounds for the quality of (probability) density estimation. Connections are established between these problems and the theory of approximation of functions. Particularly, it is demonstrated how some of Kolmogorov's concepts work.
"On Density Estimation in the View of Kolmogorov's Ideas in Approximation Theory." Ann. Statist. 18 (3) 999 - 1010, September, 1990. https://doi.org/10.1214/aos/1176347736