  We introduce a statistical quantity, known as the $K$ function, related to
the integral of the two--point correlation function. It gives us
straightforward information about the scale where clustering dominates and the
scale at which homogeneity is reached. We evaluate the correlation dimension,
$D_2$, as the local slope of the log--log plot of the $K$ function. We apply
this statistic to several stochastic point fields, to three numerical
simulations describing the distribution of clusters and finally to real galaxy
redshift surveys. Four different galaxy catalogues have been analysed using
this technique: the Center for Astrophysics I, the Perseus--Pisces redshift
surveys (these two lying in our local neighbourhood), the Stromlo--APM and the
1.2 Jy {\it IRAS} redshift surveys (these two encompassing a larger volume). In
all cases, this cumulant quantity shows the fingerprint of the transition to
homogeneity. The reliability of the estimates is clearly demonstrated by the
results from controllable point sets, such as the segment Cox processes. In the
cluster distribution models, as well as in the real galaxy catalogues, we never
see long plateaus when plotting $D_2$ as a function of the scale, leaving no
hope for unbounded fractal distributions.
