Abstract
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.
Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
