On Lipschitz and d.c. surfaces of finite codimension in a Banach space

Luděk Zajíček

On Lipschitz and d.c. surfaces of finite codimension in a Banach space

Functional Analysis 2016-08-14 v1

Authors: Luděk Zajíček

Abstract

Properties of Lipschitz and d.c. surfaces of finite codimension in a Banach space, and properties of generated $\sigma$ -ideals are studied. These $\sigma$ -ideals naturally appear in the differentiation theory and in the abstract approximation theory. Using these properties, we improve an unpublished result of M. Heisler which gives an alternative proof of a result of D. Preiss on singular points of convex functions.

Keywords

lipschitz surfaces d.c. surfaces finite codimension banach space sigma-ideals convex functions

Cite

@article{arxiv.math/0701926,
  title  = {On Lipschitz and d.c. surfaces of finite codimension in a Banach space},
  author = {Luděk Zajíček},
  journal= {arXiv preprint arXiv:math/0701926},
  year   = {2016}
}

Comments

13 pages

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