  We analyze the spatial and the luminosity properties of the Perseus-Pisces
redshift survey. We find that the two point correlation function (CF)
$\Gamma(r)$ is a power law up to the sample effective depth ($\sim 30
h^{-1}Mpc$), showing the fractal nature of the galaxy distribution in this
catalog. The fractal dimension turns out to be $D \approx 2$. We also consider
the CF $\xi(r)$ and in particular the behavior of the "{\it correlation
length}" $r_0$ ($\xi(r_{0})\equiv 1$) as function of the sample size. In this
respect we find, unambiguously, that the luminosity segregation effect is not
supported by any experimental evidence. In addition we have studied the
galaxian number-density ($n(r)$) and number-counts ($N(m)$) in the VL
subsamples finding a good agreement with the properties of a fractal
distribution. In particular our conclusion is that the $n(r)$ relation allows
to extend the analysis of the fractal nature up to a deeper depth than that
reached by the CF analysis, and, we find evidence for fractal properties up to
the limiting depth of $120-140 h^{-1} Mpc$. We stress that the $N(m)$ relation
must be studied in VL subsamples rather than in magnitude limited ones as
usually done. Finally we have considered the correlations between galaxy
positions and luminosities by means of the multifractal analysis. We find clear
evidence for self-similar behavior of the whole luminosity-space distribution.
These results confirm and extend those of Coleman \& Pietronero (1992).
