rdf-syntax-grammar
mods:
  schema location: http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
  title info:
    title: Probability in Banach Spaces
    sub title: Isoperimetry and Processes
  name:
    name part: Ledoux, Michel.
    role:
      role term: creator
  name:
    name part: Talagrand, Michel.
  name:
    name part: SpringerLink (Online service)
  type of resource: text
  genre: Electronic books.
  origin info:
    place:
      place term: gw
    date issued: 1991
    issuance: monographic
  language:
    language term: eng
  physical description:
    reformatting quality: access
    form: remote
    extent: 1 online resource (xii, 480 pages)
  abstract: 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.
  table of contents: Introduction -- Notation -- Part 0. Isoperimetric Background and Generalities -- Chapter 1. Isoperimetric Inequalities and the Concentration of Measure Phenomenon -- Chapter 2. Generalities on Banach Space Valued Random Variables and Random Processes -- Part I. Banach Space Valued Random Variables and Their Strong Limiting Properties -- Chapter 3. Gaussian Random Variables -- Chapter 4. Rademacher Averages -- Chapter 5. Stable Random Variables -- Chapter 6. Sums of Independent Random Variables -- Chapter 7. The Strong Law of Large Numbers -- Chapter 8. The Law of the Iterated Logarithm -- Part II. Tightness of Vector Valued Random Variables and Regularity of Random Processes -- Chapter 9. Type and Cotype of Banach Spaces -- Chapter 10. The Central Limit Theorem -- Chapter 11. Regularity of Random Processes -- Chapter 12. Regularity of Gaussian and Stable Processes -- Chapter 13. Stationary Processes and Random Fourier Series -- Chapter 14. Empirical Process Methods in Probability in Banach Spaces -- Chapter 15. Applications to Banach Space Theory.
  note: by Michel Ledoux, Michel Talagrand.
  note: Electronic resource.
  subject:
    topic: Mathematics
  subject:
    topic: System theory
  subject:
    topic: Mathematical optimization
  subject:
    topic: Distribution (Probability theory)
  classification: QA273.A1-274.9
  classification: QA274-274.9
  classification: 519.2
  related item:
    title info:
      title: Ergebnisse der Mathematik und ihrer Grenzgebiete, A Series of Modern Surveys in Mathematics ; 23
  identifier: 9783642202124 (electronic bk.)
  identifier: 3642202128 (electronic bk.)
  identifier: 9783642202117
  identifier: 364220211X
  identifier: 3642202128
  identifier: http://proxy.library.tamu.edu/login
  record info:
    record content source: AU@
    record creation date: 130215
    record change date: 20260422210349.1
    record identifier: in00003559874
    language of cataloging:
      language term: eng