On the density in the grand canonical ensemble

The grand canonical ensemble of one-component systems of particles contained in a field $\Lambda$ is considered. It is proved thet if density (the first correlation function) approches the finite limit when the field $\Lambda$ tends to infinity in the sense of Fisher, then under contentedly common conditions this limit is represented by the function, thet under some conditions is the analytical continuation of Mayer`s expansion, representing the density as a function of the activity.