  K.\ S.\ Lau had shown that a reflexive Banach space has the Mazur
Intersection Property (MIP) if and only if every closed bounded convex set is
the closed convex hull of its farthest points.
  In this work, we show that in general this latter property is equivalent to a
property stronger than the MIP. As corollaries, we recapture the result of Lau
and characterize the w*-MIP in dual of RNP spaces.
