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## Details

Genre/Form: | Electronic books |
---|---|

Additional Physical Format: | Print version: Lindenstrauss, Joram Frechet Differentiability of Lipschitz Functions and Porous Sets in Banach Spaces Princeton : Princeton University Press,c2012 |

Material Type: | Document, Internet resource |

Document Type: | Internet Resource, Computer File |

All Authors / Contributors: |
Joram Lindenstrauss; David Preiss; Jaroslav Tišer |

ISBN: | 9781400842698 1400842697 |

OCLC Number: | 769343169 |

Notes: | Description based upon print version of record. 14.7 Proof of Theorem |

Description: | 1 online resource (436 p.) |

Contents: | Cover; Title Page; Copyright Page; Table of Contents; Chapter 1. Introduction; 1.1 Key notions and notation; Chapter 2. Gâteaux Dfferentiability of Lipschitz Functions; 2.1 Radon-Nikodým Property; 2.2 Haar and Aronszajn-Gauss Null Sets; 2.3 Existence Results for Gâteaux Derivatives; 2.4 Mean Value Estimates; Chapter 3. Smoothness, Convexity, Porosity, and Separable Determination; 3.1 A criterion of Differentiability of Convex Functions; 3.2 Fréchet Smooth and Nonsmooth Renormings; 3.3 Fréchet Differentiability of Convex Functions; 3.4 Porosity and Nondifferentiability 3.5 Sets of Fréchet Differentiability Points3.6 Separable Determination; Chapter 4. e-Fréchet Differentiability; 4.1 e-Differentiability and Uniform Smoothness; 4.2 Asymptotic Uniform Smoothness; 4.3 e-Fréchet Differentiability of Functions on Asymptotically Smooth Spaces; Chapter 5. G-Null and Gn-Null Sets; 5.1 Introduction; 5.2 G-Null Sets and Gâteaux Differentiability; 5.3 Spaces of Surfaces; 5.4 G- and Gn-Null Sets of low Borel Classes; 5.5 Equivalent Definitions of Gn-Null Sets; 5.6 Separable Determination; Chapter 6. Fréchet Differentiability Except for G-Null Sets; 6.1 Introduction 6.2 Regular Points6.3 A Criterion of Fréchet Differentiability; 6.4 Fréchet Differentiability Except for G-Null Sets; Chapter 7. Variational Principles; 7.1 Introduction; 7.2 Variational Principles via Games; 7.3 Bimetric Variational Principles; Chapter 8. Smoothness and Asymptotic Smoothness; 8.1 Modulus of Smoothness; 8.2 Smooth Bumps with Controlled Modulus; Chapter 9. Preliminaries to Main Results; 9.1 Notation, Linear Operators, Tensor Products; 9.2 Derivatives and Regularity; 9.3 Deformation of Surfaces Controlled by ?n; 9.4 Divergence Theorem; 9.5 Some Integral Estimates Chapter 10. Porosity, Gn- and G-Null Sets10.1 Porous and s-Porous Sets; 10.2 A Criterion of Gn-nullness of Porous Sets; 10.3 Directional Porosity and Gn-Nullness; 10.4 s-Porosity and Gn-Nullness; 10.5 G1-Nullness of Porous Sets and Asplundness; 10.6 Spaces in which s-Porous Sets are G-Null; Chapter 11. Porosity and e-Fréchet Differentiability; 11.1 Introduction; 11.2 Finite Dimensional Approximation; 11.3 Slices and e-Differentiability; Chapter 12. Fréchet Differentiability of Real-Valued Functions; 12.1 Introduction and Main Results; 12.2 An Illustrative Special Case 12.3 A Mean Value Estimate12.4 Proof of Theorems; 12.5 Generalizations and Extensions; Chapter 13. Fréchet Differentiability of Vector-Valued Functions; 13.1 Main Results; 13.2 Regularity Parameter; 13.3 Reduction to a Special Case; 13.4 Regular Fréchet Differentiability; 13.5 Fréchet Differentiability; 13.6 Simpler Special Cases; Chapter 14. Unavoidable Porous Sets and Nondifferentiable Maps; 14.1 Introduction and Main Results; 14.2 An Unavoidable Porous Set in l1; 14.3 Preliminaries to Proofs of Main Results; 14.4 The Main Construction; 14.5 The Main Construction; 14.6 Proof of Theorem |

Series Title: | Annals of mathematics studies, no. 179 |

### Abstract:

## Reviews

*Editorial reviews*

Publisher Synopsis

"The book is well written--as one would expect from its distinguished authors, including the late Joram Lindestrauss (1936-2012). It contains many fascinating and profound results. It no doubt will become an important resource for anyone who is seriously interested in the differentiability of functions between Banach spaces."--J. Borwein and Liangjin Yao, Mathematical Reviews Clippings "[T]his is a very deep and complete study on the differentiability of Lipschitz mappings between Banach spaces, an unavoidable reference for anyone seriously interested in this topic."--Daniel Azagra, European Mathematical Society Read more...

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