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:
    non sort: The
    title: integrals of Lebesgue, Denjoy, Perron, and Henstock
  name:
    name part: Gordon, Russell A.
    name part: 1955-
    role:
      role term: creator
    role:
      role term: author
  type of resource: text
  genre: bibliography
  origin info:
    place:
      place term: riu
    date issued: 1994
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: print
    extent: xi, 395 pages : illustrations ; 27 cm.
  abstract: Provides an elementary, self-contained presentation of the integration processes developed by Lebesgue, Denjoy, Perron, and Henstock. The Lebesgue integral and its essential properties are first developed in detail. The other three integrals are all generalizations of the Lebesgue integral that satisfy the ideal version of the Fundamental Theorem of Calculus. The Denjoy, Perron, and Henstock integrals are each developed fully and carefully from their corresponding definitions. The last part of the book is devoted to integration processes which satisfy a theorem analogous to the Fundamental Theorem, in which F is approximately differentiable. This part of this book is preceded by a detailed study of the approximate derivative and ends with some open questions. Contains over 230 exercises (with solutions) that illustrate and expand the material in the text.
  table of contents: Ch. 1. Lebesgue measure -- Ch. 2. Measurable functions -- Ch. 3. The Lebesgue integral -- Ch. 4. Bounded variation and absolute continuity -- Ch. 5. Darboux and Baire class one functions -- Ch. 6. Functions of generalized bounded variation -- Ch. 7. The Denjoy integral -- Ch. 8. The Perron integral -- Ch. 9. The Henstock integral -- Ch. 10. The McShane integral -- Ch. 11. Equivalence of integrals -- Ch. 12. Integration by parts -- Ch. 13. Convergence theorems -- Ch. 14. Approximate derivatives -- Ch. 15. The Khintchine integral -- Ch. 16. The approximately continuous Henstock integral -- Ch. 17. The approximately continuous Perron integral -- Solutions to exercises.
  note: Russell A. Gordon.
  note: Includes bibliographical references (pages 389-390) and indexes.
  subject:
    topic: Measure theory
  subject:
    topic: Functions of real variables
  subject:
    topic: Théorie de la mesure
  subject:
    topic: Fonctions de variables réelles
  subject:
    topic: Functions of real variables
  subject:
    topic: Measure theory
  subject:
    topic: Maattheorie
  subject:
    topic: Measure and integration
  subject:
    topic: Integral calculus
  subject:
    topic: Theorems
  subject:
    topic: Entire functions
  subject:
    topic: Real variables
  subject:
    topic: Measurement
  subject:
    topic: Integrals
  subject:
    topic: Lebesgue integral
  subject:
    topic: Measure theory
  subject:
    topic: Functions of real variables
  subject:
    topic: Fonctions d'une variable réelle
  subject:
    topic: Mesure, théorie de la
  subject:
    topic: Functions of real variables
  subject:
    topic: Measure theory
  classification: QA312 .G63 1994
  classification: 515/.42
  classification: 31.41
  classification: *26A39
  classification: 26-02
  classification: 28-02
  classification: PB 90
  related item:
    title info:
      title: Graduate studies in mathematics ; v. 4
  identifier: 0821838059
  identifier: 9780821838051
  identifier: 94019080
  identifier: http://www.gbv.de/dms/hbz/toc/ht006543584.PDF
  identifier: http://www.zentralblattmath.org/zmath/en/search/
  related item:
    location:
      url: http://www.gbv.de/dms/hbz/toc/ht006543584.PDF
  related item:
    location:
      url: http://www.zentralblattmath.org/zmath/en/search/
  location:
    physical location: TAG TAGC
  record info:
    record content source: DLC
    record creation date: 940503
    record change date: 20240808145606.8
    record identifier: in00004813914
    language of cataloging:
      language term: eng