A universal differentiability set in Banach spaces with separable dual

作者：Dore Michael; Maleva Olga^*

来源：Journal of Functional Analysis, 2011, 261(6): 1674-1710.

DOI：10.1016/j.jfa.2011.05.016

• Universal differentiability set
• Frechet differentiability
• Null set

We show that any non-zero Banach space with a separable dual contains a totally disconnected, closed and bounded subset S of Hausdorff dimension 1 such that every Lipschitz function on the space is Frechet differentiable somewhere in S.

• 出版日期2011-9-15