THEORY OF APPROXIMATION OF PATTERN SETS BASED ON THE epsilon -ENTROPY THEORY.

Investigation of the approximation problem of the pattern set by means of the n-diameter and epsilon -entropy of a set, which are quantities that reflect topological characteristics of the set itself. It is found that the pattern distance derived from a norm is of a restricted type, for it must satisfy transitivity and homogeneity. Distances not obeying transitivity or homogeneity are quite conceivable, but they cannot be treated by the epsilon -entropy theory of the Hilbert space.