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TY - CHAP
TI - Unavoidable porous sets and nondifferentiable maps
AU - Lindenstrauss, Joram
AU - Preiss, David
AU - Tišer, Jaroslav
AB - In Chapters 10 and 13 we have established conditions on a Banach space*X*under which porous sets in*X*are Γ_{n}-null and/or the the multidimensional mean value estimates for Fréchet derivatives of Lipschitz maps into*n*-dimensional spaces hold. Here we show in what sense these results are close to being optimal. Under conditions that can be argued to be close to complementary to those from the previous chapters, we find a σ-porous set whose complement is null on all*n*-dimensional surfaces and the multidimensional mean value estimates fail even for*ε*-Fréchet derivatives. Particular situations in which these negative results
EP - 354
PB - Princeton University Press
PY - 2012
SN - 9780691153551
SP - 319
T2 - Frechet Differentiability of Lipschitz Functions and Porous Sets in Banach Spaces (AM-179)
UR - http://www.jstor.org/stable/j.ctt7svpc.16
Y2 - 2021/09/21/
ER -