Abstract.
In this paper we study the behaviour of two functions which can be
defined in normed spaces: they measure, for finite sets on the unit
sphere, ``average distances'' from points in smaller spheres. We also study
these functions when only pairs of opposite points are considered.
We generalize some results indicated in recent papers, concerning
the values of these functions when ``average distances'' are measured
from points in the unit sphere of the space.
Compressed Postscript 
