Some Topological And Geometrical Structures In Banach Spaces
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Some Topological and Geometrical Structures in Banach Spaces
Author: Nassif Ghoussoub
language: en
Publisher: American Mathematical Soc.
Release Date: 1987
In this memoir, we study the interrelations between the topological, measure theoretical and geometrical structures in certain classes of Banach spaces. The focus is on those spaces whose bounded subsets have arbitrarily norm-small convex combinations of slices. This class contains spaces with the Radon-Nikodym property as well as B-convex Banach spaces. The topological analysis leads to the concept of "first class functions around sets". This extension of the classical notion of Baire-1 functions is developed in a general non-linear setting.