Probability in Banach Spaces

Isoperimetry and Processes

  • Michel Ledoux
  • Michel Talagrand

Part of the Ergebnisse der Mathematik und ihrer Grenzgebiete book series (volume 23)

Table of contents

  1. Front Matter
    Pages I-XII
  2. Introduction

    1. Michel Ledoux, Michel Talagrand
      Pages 1-6
  3. Notation

    1. Michel Ledoux, Michel Talagrand
      Pages 7-12
  4. Isoperimetric Background and Generalities

    1. Front Matter
      Pages 13-13
  5. Banach Space Valued Random Variables and Their Strong Limiting Properties

    1. Front Matter
      Pages 53-53
    2. Michel Ledoux, Michel Talagrand
      Pages 54-88
    3. Michel Ledoux, Michel Talagrand
      Pages 89-121
    4. Michel Ledoux, Michel Talagrand
      Pages 122-148
    5. Michel Ledoux, Michel Talagrand
      Pages 149-177
    6. Michel Ledoux, Michel Talagrand
      Pages 178-195
    7. Michel Ledoux, Michel Talagrand
      Pages 196-234
  6. Tightness of Vector Valued Random Variables and Regularity of Random Processes

    1. Front Matter
      Pages 235-235
    2. Michel Ledoux, Michel Talagrand
      Pages 236-271
    3. Michel Ledoux, Michel Talagrand
      Pages 272-296
    4. Michel Ledoux, Michel Talagrand
      Pages 297-331
    5. Michel Ledoux, Michel Talagrand
      Pages 332-364
    6. Michel Ledoux, Michel Talagrand
      Pages 365-393
    7. Michel Ledoux, Michel Talagrand
      Pages 394-420

About this book

Introduction

Isoperimetric, measure concentration and random process techniques appear at the basis of the modern understanding of Probability in Banach spaces. Based on these tools, the book presents a complete treatment of the main aspects of Probability in Banach spaces (integrability and limit theorems for vector valued random variables, boundedness and continuity of random processes) and of some of their links to Geometry of Banach spaces (via the type and cotype properties). Its purpose is to present some of the main aspects of this theory, from the foundations to the most important achievements. The main features of the investigation are the systematic use of isoperimetry and concentration of measure and abstract random process techniques (entropy and majorizing measures). Examples of these probabilistic tools and ideas to classical Banach space theory are further developed.

Keywords

Banach Space Fourier series Law of large numbers Random variable differential equation entropy law of the iterated logarithm logarithm measure

Authors and affiliations

  • Michel Ledoux
    • 1
  • Michel Talagrand
    • 2
    • 3
  1. 1.Institut de Recherche Mathématique Avancée, Département de MathématiqueUniversité Louis PasteurStrasbourgFrance
  2. 2.Equipe d’AnalyseUniversité de Paris VIParisFrance
  3. 3.Department of MathematicsThe Ohio State UniversityColumbusUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-20212-4
  • Copyright Information Springer-Verlag Berlin Heidelberg 1991
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-642-20211-7
  • Online ISBN 978-3-642-20212-4
  • Series Print ISSN 0071-1136
  • About this book