  A continuous infinite system of point particles with strong superstable
interaction is considered in the framework of classical statistical mechanics.
The family of approximated correlation functions is determined in such a way,
that they take into account only such configurations of particles in
$\mathbb{R}^d$ which for a given partition of the configuration space
$\mathbb{R}^d$ into nonintersecting hyper cubes with a volume $a^d$ contain no
more than one particle in every cube. We prove that these functions converge to
the proper correlation functions of the initial system if the parameter of
approximation $a\rightarrow 0$ for any positive values of an inverse
temperature $\beta$ and a fugacity $z$. This result is proven both for two-body
interaction potentials and for many-body case.
