Comments on the paper “Mathematical description of the equilibrium state of classical systems on the basis of the canonical ensemble formalism” by N. N. Bogolyubov, D. Ya. Petrina, and B. I. Khatset

Some of the arguments and proofs in the paper by Bogolyubov, Petrina, and Khatset are simplified. The simplifications are achieved by the use of the apparatus of correlation functions rather than distribution functions. In addition, a more detailed investigation is made of the question of the equality of the limiting correlation functions of the microcanonical and grand canonical ensembles in the case of low densities.