On ϵ-Entropy of Sobolev and Nikolsky Classes in Uniform Metrics on Arbitrary Compacts Original Research Article

This paper is devoted to the study of ϵ-entropy of the Nikolsky classes Hα∞(Is) in C(K), where K is an arbitrary compact set in Is. For a connected set K the order of ϵ-entropy is known to be the same as the order of Komolgorov′s ϵ-dimension. Without connectedness this is not the case. The exact order is given in terms of two functions characterizing "density" and "discontinuity" of the compact K.