ε-Entropy and ε-Capacity of Sets In Functional Spaces

Abstract

The article is mainly devoted to the systematic exposition of results that were published in the years 1954–1958 by K. I. Babenko [1], A. G. Vitushkin [2,3], V. D. Yerokhin [4], A. N. Kolmogorov [5,6] and V. M. Tikhomirov [7]. It is natural that when these materials were systematically rewritten, several new theorems were proved and certain examples were computed in more detail. This review also incorporates results not published previously which go beyond the framework of such a systematization, and belong to V. I. Arnold ({\textsection}6) and V. M. Tikhomirov ({\textsection}{\textsection}4,7 and {\textsection}8).