Kolmogorov entropy for classes of convex functions (Q836088)

Kolmogorov \(\varepsilon\)-entropy of a compact set in the metric space measures its metric massivity and thus replaces its dimension which is usually infinite. The \(\varepsilon\)-entropy of a compact set is the most economic quantity of information that permits a recovery of elements of this set with accuracy \(\varepsilon\). The present article deals with the study of the problem of asymptotic behavior of the \(\varepsilon\)-entropy for uniformly bounded classes of convex functions in \(L_p\) metric. The asymptotic of the Kolmogorov \(\varepsilon\)-entropy for the compact metric space of convex and uniformly bounded functions equipped with \(L_p\) metric is \(\varepsilon^{-1/2}\), \(\varepsilon\rightarrow0_+.\)