Porosity and ε-Fr échet differentiability
Porosity and ε-Fr échet differentiability
This chapter demonstrates that the results about smallness of porous sets, and so also of sets of irregularity points of a given Lipschitz function, can be used to show existence of points of (at least) ε-Fréchet differentiability of vector-valued functions. The approach involves combining this new idea with the basic notion that points of ε-Fréchet differentiability should appear in small slices of the set of Gâteaux derivatives. The chapter obtains very precise results on existence of points of ε-Fréchet differentiability for Lipschitz maps with finite dimensional range. The main result applies when every porous set is contained in the unions of a σ-directionally porous (and hence Haar null) set and a Γₙ-null Gsubscript Small Delta set.
Keywords: porous sets, irregularity point, Lipschitz function, ε-Fréchet differentiability, slice, Gâteaux derivative, Lipschitz map
Princeton Scholarship Online requires a subscription or purchase to access the full text of books within the service. Public users can however freely search the site and view the abstracts and keywords for each book and chapter.
Please, subscribe or login to access full text content.
If you think you should have access to this title, please contact your librarian.
To troubleshoot, please check our FAQs , and if you can't find the answer there, please contact us.
