The Barycentric Selection on Non-negative Lebesgue Integrable Function of Set-valued Map

The definitions of the barycentric selection on non-negative integrable function of the set-valued map are introduced.Some properties of the barycentric selection are discussed.On this basis,the barycentric selection are expanded to the generalized form: for the arbitrary r∈R+,a Lipschitz selection of set-valued map with compact convex images is given,and its properties are proved.