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.
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