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TY - CHAP
TI - Γ-null and Γn-null sets
AU - Lindenstrauss, Joram
AU - Preiss, David
AU - Tišer, Jaroslav
AB - We define the notions of Γ- and Γ_{n}-null sets that will play a major role in our investigations of the interplay between differentiability, porosity, and smallness on curves or surfaces. Here we relate these notions to Gâteaux differentiability and investigate their basic properties. Somewhat unexpectedly, we discover an interesting relation between Γ- and Γ_{n}-null*G*_{δσ}sets, and this will turn out to be very useful in finding a new class of spaces for which the strong Fréchet differentiability result holds in Theorem 10.6.2. In this chapter we introduce σ-ideals of subsets of a Banach space*X*called Γ-null sets or
EP - 95
PB - Princeton University Press
PY - 2012
SN - 9780691153551
SP - 72
T2 - Frechet Differentiability of Lipschitz Functions and Porous Sets in Banach Spaces (AM-179)
UR - http://www.jstor.org/stable/j.ctt7svpc.7
Y2 - 2021/09/27/
ER -