On the \(\varepsilon\)-entropy and diameters of a compactum of smooth functions in the space of functions of bounded \(p\)-variation
A generalization of the results due to \textit{A. P. Terekhin} [Izv. Vyssh. Uchebn. Zaved. Mat. 1965, 2(45), 171-187 (1965; Zbl 0156.068)] is presented and by the methods of \textit{G. G. Lorentz} [Bull. Am. Math. Soc. 72, No. 6, 903-937 (1966; Zbl 0158.136)] two-sided estimations of \(\varepsilon\)-entropy are obtained and next upper and lower estimations of diameters are presented.
two-sided estimation of \(\varepsilon\)-entropy
scientific article; zbMATH DE number 220202