Quasi-lattice approximation of statistical systems with strong superstable interactions. Correlation functions

A continuous infinite system of point particles interacting via two-body strong superstable potential is considered in the framework of classical statistical mechanics. We define some kind of approximation of main quantities, which describe macroscopical and microscopical characteristics of systems, such as grand partition function and correlation functions. The pressure of an approximated system converge to the pressure of the initial system if the parameter of approximation $a\to 0$ for any values of an inverse temperature $\beta >0$ and a chemical activity $z$. The same result is true for the family of correlation functions in the region of small z