Characterization of spannability of functions

Possibility of representation of a value of convexification of function at the given point as a convex combination of the values of function (spannability) is studied. Spannability of functions turned out to be important in different fields e.g. in the study of quasi-cores of monetary economies with nonconvex preferences (mathematical economics), in the theory of relaxation of variation problems (variational calculus). Apparently, Shapley and Shubik (Econometrica, 1966, 34, 805-827) were first to discuss it.