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: Measure theory and integration
  name:
    name part: Carpignani, Andrea
    role:
      role term: creator
    role:
      role term: author.
  name:
    name part: Taylor & Francis
  type of resource: text
  genre: bibliography
  genre: Electronic books.
  origin info:
    place:
      place term: flu
    date issued: 2026
    copyright date: 2026
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: remote
    extent: 1 online resource (326 pages) : illustrations
  abstract: This book offers a rigorous, comprehensive, and modern presentation of the most traditional concepts in measure theory and integration. Building on the classical foundations, it introduces the theory with full generality and meticulous attention to detail, following the stylistic tradition first introduced by Nicolas Bourbaki. The book is designed for graduate students and young researchers seeking a thorough exposition of the theory in an abstract setting, complete proofs, and the strategies underlying them, fostering good mathematical habits in logical reasoning and clarity of deduction.Beyond standard treatments, Measure Theory and Integration features several distinctive elements: some classical results, such as Radon-Nikodm theorem, and Lebesgue and Hahn decompositions, have been presented with original proofs, aimed at clarifying the logic behind the results; some topics that are often overlooked, such as kernels, uniform integrability, the Vitali-Hahn-Saks and Dunford-Pettis theorems are developed in full in dedicated chapters, and a complete account of the disintegration of measures is developed. The book also pays special attention to modern applications, including the construction of product measures for an arbitrary family of measures, by exploiting the properties of kernels, a full account of Daniell's and Carathodory's methods for constructing and extending measures, and a thorough coverage of the theory of convergence, and shows two paramount applications of the theory to the presentation of the Lebesgue measure and the family of Hausdorff measures.The book is largely self-contained, with supplementary sections on topology and differential calculus, and an appendix on filters and ultrafilters also included to help the reader to fully understand the notion of convergence with respect to a filter.
  note: Andrea Carpignani.
  note: "A Chapman & Hall book."
  note: Includes bibliographical references and index.
  subject:
    topic: Measure theory
  subject:
    topic: Théorie de la mesure
  subject:
    topic: Measure theory
  classification: QC20.7.M43 C37 2026
  classification: 515/.42
  identifier: 9781040809877
  identifier: 1040809871
  identifier: 9781003724766
  identifier: 1003724760
  identifier: 1040809863
  identifier: 9781040809860
  identifier: 9781041208990
  identifier: 9781003724766 Taylor & Francis
  identifier: http://proxy.library.tamu.edu/login
  record info:
    record content source: UKMGB
    record creation date: 260311
    record change date: 20260630162109.0
    record identifier: in00005786627
    language of cataloging:
      language term: eng