Quasicontinuous approximation in classical statistical mechanics

Within the framework of classical statistical mechanics, we consider infinite continuous systems of point particles with strong superstable interaction. A family of approximate correlation functions is defined to take into account solely the configurations of particles in the space ${{\mathbb R}^d}$ that contain at most one particle in each cube of a given partition of the space ${{\mathbb R}^d}$ into disjoint hypercubes of volume a ^d: It is shown that the approximations of correlation functions thus defined are pointwise convergent to the exact correlation functions of the system if the parameter of approximation a approaches zero for any positive values of the inverse temperature β and fugacity z: This result is obtained both for two-body interaction potentials and for many-body interaction potentials.