  We investigate the statistical properties of the APM-Stromlo redshift survey
by using the concepts and methods of modern Statistical Physics. We find that
galaxy distribution in this survey exhibits scale invariant properties with
fractal dimension $D = 2.1 \pm 0.1$, up to $\sim 40 \hmp$, i.e. the limit of
its statistical validity, without any tendency towards homogenization. No
intrinsic characteristic scales are definitely found in this galaxy sample. We
present several tests to study the statistical reliability of the results. \
