On one representation of classes of distribution functions

Let $\unicode{xA3}$ be a closed convex class of distribution functions on $[0,+8),~D_n\,\unicode{xA3},~ n\geq 1,$ be a set of convex linear combinations of no more than $n$ extremal points of the $\unicode{xA3}$ class. in the present paper a representation of the $\unicode{xA3}$ class is obtained in terms of the sets.