Geodesic
AVERAGING AT ANY LEVEL
Acta mathematica Universitatis Comenianae, Tome 70 (2001) no. 2 
P.L. Papini. AVERAGING AT ANY LEVEL. Acta mathematica Universitatis Comenianae, Tome 70 (2001) no. 2. http://geodesic.mathdoc.fr/item/AMUC_2001_70_2_a11/
@article{AMUC_2001_70_2_a11,
     author = {P.L. Papini},
     title = {AVERAGING {AT} {ANY} {LEVEL}},
     journal = {Acta mathematica Universitatis Comenianae},
     year = {2001},
     volume = {70},
     number = {2},
     url = {http://geodesic.mathdoc.fr/item/AMUC_2001_70_2_a11/}
}
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Voir la notice de l'article provenant de la source Comenius University

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.