  An important problem in the analysis of experimental data showing fractal
properties, is that such samples are composed by a set of points limited by an
upper and a lower cut off. We study how finite size effect due to the
discreteness of the sets may influence self similar properties even far from
these cut-offs. Estimations of these effects are provided on the basis of the
characteristics of the samples. In particular we present an estimate of the
length scale above which information about average quantities is reliable, by
explicitly computing discreteness effects in number counting . The results have
particular importance in the statistical analysis of the distribution of
galaxies.
