Some important inequalities for estimation of the probability of correct recognition have been proposed. 
It has been marked that any recognition algorithm, using statistical methods in pattern recognition 
could be substitute by a recognition algorithm, using generalised metrical classifier. 
The main peculiarity of generalised classifier is using of the distributions of distances 
between objects and parts of cumulative density functions of these distributions.
Pointed estimates were calculated using the specific of distance distributions. 
The simple threshold classification algorithm, using principles of generalised metrical classifier has been proposed.