Relativistic corrections to fractal analyses of the galaxy distribution

The effect of curvature on the results of fractal analyses of the galaxy di stribution is investigated. We show that, if the universe satisfies the cri teria of a wide class of parabolic homogeneous models, the observers measur ing the fractal index with the integrated conditional density procedure may use the Hubble formula, without having to allow for curvature, out to dist ances of 600 Mpc, and possibly far beyond. This contradicts a previous clai m by Ribeiro (1995) that, in the Einstein-de Sitter case, relativistic corr ections should be taken into account at much smaller scales. We state for t he class of cosmological models under study, and give grounds for conjectur e for others, that the averaging procedure has a smoothing effect and that, therefore, the redshift-distance relation provides an upper limit to the r elativistic corrections involved ill such analyses.