We consider the sequence of the hyperspheres Mn,r i.e. the homogeneous transitive spaces of the Cartan subgroup SDiag(n, R) of the group SL(n, R), n = 1 . . . , and studied the normalized limit of the corresponding sequence of the invariant measures mn on those spaces. In the case of compact groups and homogeneous spaces, as example for classical pairs (SO… (More)