  Let G be a semisimple Lie group without compact factors, \Gamma be an
irreducible lattice in G. In the first part of the article we give the
necessary and sufficient condition under which a sequence of translates of
probability "horospherical measures" is convergent. And the limiting measure is
also determined when it is convergent (see Theorems 1 and 2 for the precise
statements). In the second part, two applications are presented. The first one
is of geometric nature and the second one gives an alternative way to count the
number of rational points on a flag variety.
