  Fix a density d in (0,1], and let F_p^n be a finite field, where we think of
p fixed and n tending to infinity. Let S be any subset of F_p^n having the
minimal number of three-term progressions, subject to the constraint |S| is at
least dp^n. We show that S must have some structure, and that up to o(p^n)
elements, it is a union of a small number of cosets of a subspace of dimension
n-o(n).
