2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/99009A Banach space X has the average distance property (ADP) if there exists a unique real number r such that for each positive integer n and all x_1,...,x_n in the unit sphere of X there is some x in the unit sphere of X such that 1/n \sum_{k=1}^n ||x_k-x|| = r. We show that l_p does not have the average distance property if p>2. This completes the study of the ADP for l_p spaces.10 pages, to appear in Bull. Austr. Math. SocFunctional Analysis46B20; 51K99; 52A21text