A note on non-support points, negligible sets, Gateaux differentiability and Lipschitz embeddings

作者：Cheng Lixin; Zhang Wen^*

来源：Journal of Mathematical Analysis and Applications, 2009, 350(2): 531-536.

DOI：10.1016/j.jmaa.2007.12.046

• Negligible closed convex sets
• Non-support points
• Gateaux differentiability
• Lipschitz mapping
• Banach spaces

This paper first presents a characterization of three classes of negligible closed convex sets (i.e., Gauss null sets, Aronszajn null sets and cube null sets) in terms of non-support points; then gives a generalization of Gateaux differentiability theorems of Lipschitz mapping from open sets to those closed convex sets admitting non-support points; and as their application, finally shows that a closed convex set in a separable Banach space X can be Lipschitz embedded into a Banach space Y with the Radon-Nikodym property if and only if the closure of its linear span is linearly isomorphic to a closed subspace of Y.

• 出版日期2009-2-15
• 单位厦门大学