Equivalence of integral equations in the molecular theory of fluids

It is proven that, under physically reasonable conditions, the correlation functions satisfying the BBGKY equations for an infinite system are also solutions of the Mayer-Montroll and Kirkwood-Salsburg equations. The relation between these correlation functions and the probability distributions for finding a fixed number of particles in a given finite region of an infinite system is investigated. The Gibbsian nature of these probability distributions is shown to depend on the range of the intermolecular forces.