Journal of Statistical Physics, Vol. 36, Nos. 3/4, 1984, p. 471-488.
It is shown that the basic assumptions of the classical density functional approach are rigorously correct for H-stable systems in the grand canonical ensemble. Moreover, it is established that the set of all single-particle densities is convex. These results are derived by providing necessary and sufficient conditions for the solution of the classical inverse problem for single-particle densities. Analogous results are obtained for the solution of the higher-order correlation inverse problem, and the ramifications of these results for the validity of two-body decomposition of forces are discussed.