Analytical expressions for the rates of formation and destruction of gravitationally bound systems are derived assuming that they are originated from primordial random-Gaussian density fluctuations .
The resulting formulae reproduce the time derivative of the Press-Schechter mass function in a certain limit .
Combining a theoretical model for the evolution of structures with the formation rate , we can make various cosmological predictions which are to be compared with observations .
As an example to elucidate such applicability , we evaluate the contribution of clusters of galaxies to the cosmic X-ray background radiation .
With the COBE normalization , we find that the significant fraction of the observed soft X-ray background is accounted for by clusters of galaxies in a cold dark matter universe with \Omega _ { 0 } \sim 0.2 , \lambda _ { 0 } = 1 - \Omega _ { 0 } and h \sim 0.8 .