Limit distribution functions of systems with many-particle interaction in classical statistical physics

For infinite systems of hard balls with many-particle interaction described by potentials with sufficiently rapid decreasing at the infinity, the existence of the limit distribution functions is proved as well as the existence of the generating functional of these functions, satisfying the system of functional equations which represent the generalization of the N. N. Bogoliubov equation for the generating functional of a system with the two-particle interaction.