Entropies of Sets of Functions of Bounded Variation

In this paper the entropies of several sets of functions of bounded variation are calculated. The entropy of a metric set, a notion first introduced by Kolmogorov in (2), is a measure of its size in terms of the minimal number of sets of diameter not exceeding 2∊ necessary to cover it. Using this notion, Kolmogorov (4; p. 357) and Vituškin (7) have shown that not all functions of n variables can be represented by functions of fewer variables if only functions satisfying certain smoothness conditions are allowed.