  Counts of galaxies as a function of apparent magnitude are among the most
time-honored observations in cosmology. In this Letter, we focus on some
statistical properties of these counts which are fundamental in order to
characterize the large scale correlations in the galaxy spatial distribution.
There are, in fact, no longer doubts since two decades of the existence of very
large scale structures. The still remaining problem concerns the correct
characterization of their statistical properties. We propose to study two
properties of galaxy counts data, in order to discriminate between a small
scale (~ 5 - 20 Mpc/h) homogeneous distribution, and a fractal structure on
large scales (~ 20 - 300 Mpc/h). Firstly, the average slope of the counts which
can be associated to an eventual fractal dimension in real space by simple
arguments. Secondly, we propose to study fluctuations of counts around the
average behavior as a function of apparent magnitude in the whole magnitude
range B_j > 11. These fluctuations can discriminate between a genuine fractal
distribution and a homogeneous one. In fact, they are related to the very
statistical properties of the spatial distribution, independently on
cosmological corrections. More specifically, in a fractal distribution one
expects to find persistent scale-invariant fluctuations around the average
behavior, which do not decay with apparent magnitude. On the other hand, in an
homogeneous distribution, on large enough scales, the relative variance of the
counts should decrease exponentially with apparent magnitude. Smooth
cosmological corrections cannot change such a behavior.
