Scaling properties of discrete fractals

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.