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Fréchet Differentiability of Lipschitz Functions and Porous Sets in Banach Spaces (AM-179)
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Fréchet Differentiability of Lipschitz Functions and Porous Sets in Banach Spaces (AM-179)

Joram Lindenstrauss, David Preiss, and Jaroslav Tier

Abstract

This book makes a significant inroad into the unexpectedly difficult question of existence of Fréchet derivatives of Lipschitz maps of Banach spaces into higher dimensional spaces. Because the question turns out to be closely related to porous sets in Banach spaces, it provides a bridge between descriptive set theory and the classical topic of existence of derivatives of vector-valued Lipschitz functions. The topic is relevant to classical analysis and descriptive set theory on Banach spaces. The book opens several new research directions in this area of geometric nonlinear functional analysis ... More

Keywords: descriptive set theory, Fréchet derivative, Lipschitz map, Banach space, higher dimensional space, Fréchet differentiability, Lipschitz function, nonlinear functional analysis

Bibliographic Information

Print publication date: 2012 Print ISBN-13: 9780691153551
Published to Princeton Scholarship Online: October 2017 DOI:10.23943/princeton/9780691153551.001.0001

Authors

Affiliations are at time of print publication.

Joram Lindenstrauss, author
Hebrew University of Jerusalem

David Preiss, author
University of Warwick

Jaroslav Tier, author