  I compare the numerical multiplicity function given in Yahagi, Nagashima &
Yoshii (2004) with the theoretical multiplicity function obtained by means of
the excursion set model and an improved version of the barrier shape obtained
in Del Popolo & Gambera (1998), which implicitly takes account of total angular
momentum acquired by the proto-structure during evolution and of a non-zero
cosmological constant. I show that the multiplicity function obtained in the
present paper, is in better agreement with Yahagi, Nagashima & Yoshii (2004)
simulations than other previous models (Sheth & Tormen 1999; Sheth, Mo & Tormen
2001; Sheth & Tormen 2002; Jenkins et al. 2001) and that differently from some
previous multiplicity function models (Jenkins et al. 2001; Yahagi, Nagashima &
Yoshii 2004) it was obtained from a sound theoretical background.
