  The formalism by Press and Schechter (PS) is often used to infer number
densities of virialized objects of mass M (e.g. quasars, galaxies, clusters of
galaxies, etc.) from a count of initially overdense regions in a Gaussian
density perturbation field. We reanalyze the PS-formalism by explicitly
counting underdense regions which are embedded within overdense regions, so
called cloud-in-clouds. In contrast to the original PS-formalism, our revised
analysis automatically accounts for all the cosmic material. We find that mass
distribution functions for virialized objects are altered by the proper
solution of the cloud-in-cloud problem. These altered distribution functions
agree much better with distribution functions inferred form N-body simulations
than the original PS-distribution functions.
