Isomorphism of pairs of admissible objects in pattern recognition problems

The concept of permissible object pair isomorphism for recognition problems is considered. It is known, that the pairwise non-isomorphism condition of permissible objects in a current sampling $\tilde S^q$ is necessary to prove the correctness of algebraic closure of computational algorithms of estimates. The probability that, at least, one pair of isomorphic objects with respect to the initial information $I_0$ will be found in $\tilde S^q$, is examined. The upper estimates for such a probability are obtained if $\rho_i(x,y)=|x-y|$ are considered as metrics $\rho_i$ in feature space.