  Nathanial Brown introduced a convex-like structure on the set of unitary
equivalence classes of unital *-homomorphisms of a separable type II_1 factor
into R^\omega (ultrapower of the hyperfinite factor). The goal of this paper is
to introduce such a structure on the set of sofic representations of groups. We
prove that if the commutant of a representation acts ergodicaly on the Loeb
measure space then that representation is an extreme point.
