The $\delta$-homogeneity of the Patterson measure is used for a closer study of the limit sets of Kleinian groups. A combination of the concepts of this measure with concepts of diophantine approximations is shown to lead to a more detailed understanding of these limit sets. In particular, it is seen to how great an extent the studies of these sets, in terms of Hausdorff measure or Hausdorff dimension, are limited in a natural way.