基于集值映射的非负Lebesgue可积函数的重心选择

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

首先给出了集值映射的非负Lebesgue可积函数相关的重心选择的定义,然后对重心选择的各种性质进行了讨论,在此基础上,把重心选择方法扩展到更一般的形式上,对于任意r∈R+给出了具有紧凸像的集值映射F的一个Lipschitz选择,证明了性质.

The definitions of the barycentric selection on non-negative integrable function of the set-valued map are introduced. Some properties of the barycentrie 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.