On the complexity of an approximative realization of functional compacts in some spaces and the existence of functions with given order conditions of their complexity

The question of the complexity of an approximative computation of functions from various functional compacts by schemes, consisting of continuous functions realizing elements was investigated. It was proved that almost all functions from many compacts (respectively some Kolmogorov's measure) had asymptotically equal complexity, which was equal to the complexity of the most complicated functions from these compacts. It was proved that in considered compacts there exist the functions, which have $\varepsilon$-approximation complexity asymptotically equal to $L(\varepsilon)$, under some natural restrictions.