摘要
本文在可度量化局部凸空间(特别地,F réchet空间)中引入d一致可微性并证明了连续凸函数的d一致可微点集是Borel集.最后,在RN空间中,我们证明连续凸函数的F réchet可微点集与d一致可微点集一致.
This paper defines a new kind of differentiability-d-uniform differentiability-in Fréchet spaces, and shows that the collection of d-uniform differentiability points of continuous convex functions is a Borel set. and coincides with the collection of Fréchet differentiability points in R^N.
出处
《数学研究》
CSCD
2005年第4期378-382,共5页
Journal of Mathematical Study
基金
国家自然科学基金资助项目(10471114)
关键词
凸函数
Fréchet可微性
d一致可微性
局部凸空间
convex function
Fréchet differentiability
d-uniform differentiability
locally convex space
