摘要
本文首先讨论d—凸函数为凸函数的充要条件,得到了d—凸函数为凸函数当且仅当它局部可测;进而证明了可加函数为连续的充要条件是其图象在R^2中不稠。
In this paper, firstly, we show that a d-convex function is a convex function if and only it it is a locally measurable function. Secondly, we give the necessary and sufficient conditions of continuity of additive function, we prove that an additive funclion is a linear funclion iff its graph is not dense in R^2.
关键词
可加函数
d-凸函数
凸函数
连续
d—convexfunction, Convexfunction, Additive function, Localcy measurable function.