  The Press-Schechter(PS) formalism for the mass function of the collapsed
objects are reanalyzed. The factor of two in the Press-Schechter formalism is
argued to be correct in the sharp $k$-space filter even when we use the another
approach proposed by Jedamzik(1994) in the cloud-in-cloud problem, which is
different from the previous approach by Peacock & Heavens(1990) and Bond et
al.(1991). The spatial correlation of the density fluctuations, however, had
been neglected in the cloud-in-cloud problem. The effects of this spatial
correlation is analyzed by using the Jedamzik formalism and it is found that
this effect alter the PS mass function especially on larger mass scales.
Furthermore the exact formula of deriving mass function is shown. We also find
that the probability of the overlap of the collapsed objects can be neglected
on very small mass scales while it might not be neglected on other mass scales.
