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

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	A note on non-support points, negligible sets, Gateaux differentiability and Lipschitz embeddings
	Cheng, L. X. ; Zhang, W. ; Zhang W(张文)
刊名	http://dx.doi.org/10.1016/j.jmaa.2007.12.046
	2009-02-15
关键词	GAUSSIAN NULL SETS CONVEX-FUNCTIONS BANACH-SPACES MAPPINGS
英文摘要	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. (C) 2007 Elsevier Inc. All lights reserved.
语种	英语
内容类型	期刊论文
源URL	[http://dspace.xmu.edu.cn/handle/2288/66251]
专题	数学科学－已发表论文
推荐引用方式 GB/T 7714	Cheng, L. X.,Zhang, W.,Zhang W. A note on non-support points, negligible sets, Gateaux differentiability and Lipschitz embeddings[J]. http://dx.doi.org/10.1016/j.jmaa.2007.12.046,2009.
APA	Cheng, L. X.,Zhang, W.,&张文.(2009).A note on non-support points, negligible sets, Gateaux differentiability and Lipschitz embeddings.http://dx.doi.org/10.1016/j.jmaa.2007.12.046.
MLA	Cheng, L. X.,et al."A note on non-support points, negligible sets, Gateaux differentiability and Lipschitz embeddings".http://dx.doi.org/10.1016/j.jmaa.2007.12.046 (2009).