  Let \Gamma be a lattice in G=SL(n,R) and X=G/S a homogeneous space of G,
where S is a closed subgroup of G which contains a real algebraic subgroup H
such that G/H is compact. We establish uniform distribution of orbits of \Gamma
in X analogous to the classical equidistribution on torus. To obtain this
result, we first prove an ergodic theorem along balls in the connected
component of Borel subgroup of G.
