If S is a left amenable
semigroup, let ML(S) be the set of left invariant means on m(S), the space of
bounded real-valued functions on S. We prove in this paper that a left invariant
mean on m(S) is an exposed point of ML(S) if and only if it is the arithmetic
average on a minimal finite left ideal of S. In particular, ML(S) has no
exposed point when S is an infinite group. We also prove that if ML(S) has an
exposed point, then it is the w∗-closed convex hull of all its exposed points.
This gives another proof of the Granirer-Klawe theorem on the dimension of
ML(S).
