Choquet like sets in function spaces

In convex analysis when studying function spaces of continuous affine functions, notions of a geometrical character like faces, split and parallel faces, exposed or Archimedean faces were investigated in detail by many authors. In this paper we transfer these notions to a more general setting of Choquet theory of abstract function spaces. We prefer a direct functional analytic approach to the treatment of problems instead of using a transfer of a function space to its state space. Methods invoked are based mainly on a measure theory and basic tools of functional analysis and are different from ones using a geometric visualization.