**B. Aronov, F. Aurenhammer, F. Hurtado, S. Langerman, D. Rappaport,
S. Smorodinsky, and C. Seara**

Let S be a family of sets in the plane. Let 0 < epsilon(S,i) < 1 denote the
minimum real number such that for any finite point set P there exists a set Q
of i points that is a weak epsilon(S,i)-net for P with respect to S. We
derice upper and lower bounds on epsilon(S,i) for small integers i and when S
is the family of all convex sets, or the family of all axis-parallel
rectangles.