摘要
本文证明了如果可分Banach空间E的每个开凸子集D上的连续凸函数都在D中某一点β可微，则E*的每个有界弱.闭凸子集关于其上弱于或等于由β导出的拓扑τβ的距离是可分的．
In this paper, it is proved that if E is separable and each continuous convex function on every open convex subset D of E is βdifferentiable at some point in D,then each weak compact convex subset of E is separable with respect to a metric which is weaker than or equal to the topology induced by β
出处
《华南师范大学学报（自然科学版）》
CAS
1999年第1期21-25,共5页
Journal of South China Normal University(Natural Science Edition)
关键词
凸函数
β可微
巴拿赫空间
连续凸函数
築anach space； convex function,β differentiability, separable
