  Here we try and delienate the properties of the function that corresponds to
fluctuations in the momentum distribution. The quantity denoted by $ N(k,k^{'})
$ is quite an interesting object. It satisfies various elegant sum rules and is
also quite singular in some respects. All these properties are brought out and
a formal connection is found between this object and the momentum distribution
of the interacting and non-interacting many-fermion systems. This exercise is
quite general in that it does not refer to any particular hamiltonian. It is
also quite useful since in an earlier preprint(cond-mat/9810043) we showed how
to compute the spectral function and single-particle lifetime of homogeneous
Fermi systems where the only undetermined quantity was this function $
N(k,k^{'}) $.
