  Let S be a set of n points in the plane, and let T be a set of m triangles
with vertices in S. Then there exists a point in the plane contained in
Omega(m^3 / (n^6 log^2 n)) triangles of T. Eppstein (1993) gave a proof of this
claim, but there is a problem with his proof. Here we provide a correct proof
by slightly modifying Eppstein's argument.
