Banach空间中连续凸函数的Gateaux可微性的一个注记(英文)

A Note To Gateaux Differentiability Of Convex Continuous Function On Banach Space

给出并证明了：若Banach空间中开凸子集上定义的连续凸函数在其一个稠集上Gateaux可微，则它一定在其一个稠Gδ集上Gateaux可微。

In this paper, it is shown that if a convex continuous function on Banach space defiend on an open convex subset of D is Gateaux differentiable on a dense subset of its domain, the function is Gateaux differentiable on a dense Gδ subset.