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: An
    title: introduction to measure-theoretic probability
  name:
    name part: Roussas, George G.
    role:
      role term: creator
    role:
      role term: author.
  name:
    name part: ScienceDirect (Online service)
  type of resource: text
  genre: bibliography
  genre: Electronic books.
  origin info:
    place:
      place term: ne
    date issued: 2014
    edition: Second edition.
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: remote
    extent: 1 online resource
  abstract: "In this introductory chapter, the concepts of a field and of a [sigma]-field are introduced, they are illustrated bymeans of examples, and some relevant basic results are derived. Also, the concept of a monotone class is defined and its relationship to certain fields and [sigma]-fields is investigated. Given a collection of measurable spaces, their product space is defined, and some basic properties are established. The concept of a measurable mapping is introduced, and its relation to certain [sigma]-fields is studied. Finally, it is shown that any random variable is the pointwise limit of a sequence of simple random variables"--
  table of contents: Certain classes of sets, measurability, and pointwise approximation -- Definition and construction of a measure and its basic properties -- Some modes of convergence of sequences of random variables and their relationships -- The integral of a random variable and its basic properties -- Standard convergence theorems, the Fubini theorem -- Standard moment and probability inequalities, convergence in the rth mean and its implications -- The Hahn-Jordan decomposition theorem, the Lebesgue decomposition theorem, and the Radon-Nikodym theorem -- Distribution functions and their basic properties, Helly-Bray type results -- Conditional expectation and conditional probability, and related properties and results -- Independence -- Topics from the theory of characteristic functions -- The central limit problem: the centered case -- The central limit problem: the noncentered case -- Topics from sequences of independent random variables -- Topics from Ergodic theory -- Two cases of statistical inference: estimation of a real-valued parameter, nonparametric estimation of a probability density function -- Appendixes: A. Brief review of chapters 1-16 -- B. Brief review of Riemann-Stieltjes integral -- C. Notation and abbreviations.
  note: by George G. Roussas.
  note: Includes bibliographical references and index.
  subject:
    topic: Probabilities
  subject:
    topic: Measure theory
  subject:
    topic: Probabilités
  subject:
    topic: Théorie de la mesure
  subject:
    topic: probability
  subject:
    topic: Measure theory
  subject:
    topic: Probabilities
  classification: QA273 .R864 2014eb
  classification: 519.2
  related item:
    title info:
      title: Introduction to measure-theoretic probability
    name:
      name part: Roussas, George G.
    origin info:
      edition: Second edition
    identifier: (DLC) 2014007243
    identifier: (OCoLC)868642456
  identifier: 9780128002902
  identifier: 0128002905
  identifier: 9780128000427
  identifier: D5449F71-F849-4749-93C1-41290688DB70 OverDrive, Inc.
  identifier: http://proxy.library.tamu.edu/login
  record info:
    record content source: OPELS
    record creation date: 140414
    record change date: 20260326200535.4
    record identifier: in00005754258
    language of cataloging:
      language term: eng