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, integral, and probability
  name:
    name part: Capiński, Marek
    name part: 1951-
    role:
      role term: creator
  name:
    name part: Kopp, P. E.
    name part: 1944-
  name:
    name part: SpringerLink (Online service)
  type of resource: text
  genre: bibliography
  genre: Electronic books.
  origin info:
    place:
      place term: enk
    date issued: 1999
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: remote
    extent: 1 online resource (xi, 227 pages) : illustrations.
  abstract: The key concept is that of measure which is first developed on the real line and then presented abstractly to provide an introduction to the foundations of probability theory (the Kolmogorov axioms) which in turn opens a route to many illustrative examples and applications, including a thorough discussion of standard probability distributions and densities. Throughout, the development of the Lebesgue Integral provides the essential ideas: the role of basic convergence theorems, a discussion of modes of convergence for measurable functions, relations to the Riemann integral and the fundamental theorem of calculus, leading to the definition of Lebesgue spaces, the Fubini and Radon-Nikodym Theorems and their roles in describing the properties of random variables and their distributions. Applications to probability include laws of large numbers and the central limit theorem.
  table of contents: Preface -- Motivation and Preliminaries -- Measure -- Measurable Functions -- Integral -- Spaces of Integral Functions -- Product Measures -- Limit Theorems -- Index -- Literature.
  note: Marek Capiński and Ekkehard Kopp.
  note: Includes bibliographical references (page 223) and index.
  subject:
    topic: Measure theory
  subject:
    topic: Integrals, Generalized
  subject:
    topic: Probabilities
  subject:
    topic: Mesure, Théorie de la
  subject:
    topic: Intégrales généralisées
  subject:
    topic: Probabilites
  subject:
    topic: Wahrscheinlichkeitstheorie
  subject:
    topic: Ma€theorie
  subject:
    topic: Lebesgue-Integral
  subject:
    topic: Integrals, Generalized
  subject:
    topic: Measure theory
  subject:
    topic: Probabilities
  classification: QA312 .C36 1999eb
  classification: 515/.42
  classification: 27
  classification: MAT 280f
  classification: MAT 600f
  classification: SK 430
  related item:
    title info:
      title: Measure, integral, and probability
    name:
      name part: Capiński, Marek, 1951-
    identifier: (DLC) 98034763
    identifier: (OCoLC)39625247
  related item:
    title info:
      title: Springer undergraduate mathematics series
  identifier: 9781447136316 (electronic bk.)
  identifier: 1447136314 (electronic bk.)
  identifier: 3540762604
  identifier: 9783540762607
  identifier: http://proxy.library.tamu.edu/login
  record info:
    record content source: GW5XE
    record creation date: 131029
    record change date: 20260420202959.5
    record identifier: in00003562162
    language of cataloging:
      language term: eng