Asymptotics for the minimum riesz energy and best-packing on sets of finitie packing premeasure

We show that for every compact set A ⊂ Rm of finite α -dimensional packing premeasure 0 < α ≤m, the lower limit of the normalized discrete minimum Riesz s-energy (s > α ) coincides with the outer measure of A constructed from this limit by method I. The asymptotic behavior of the discrete minimum energy on compact subsets of a self-similar set K satisfying the open set condition is also studied for s greater than the Hausdor dimension of K. In addition, similar problems are studied for the best-packing radius.