Advertisement

Classes of Sets, Measures, and Probability Spaces

  • Yuan Shih Chow
  • Henry Teicher
Chapter
  • 1.7k Downloads
Part of the Springer Texts in Statistics book series (STS)

Abstract

A set, in the words of Georg Cantor, the founder of modern set theory, is a collection into a whole of definite, well-distinguished objects of our perception or thought, The objects are called elements and the set is the aggregate of these elements. It is very convenient to extend this notion and also envisage a set devoid of elements, a so-called empty set, and this will be denoted by 0. Each element of a set appears only once therein and its order of appearance within the set is irrelevant. A set whose elements are themselves sets will be called a class.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. J. L. Doob, “Supplement,”Stochastic ProcessesWiley, New York, 1953.Google Scholar
  2. E. B. DynkinTheory of Markor Processes(D. E. Brown, translator), Prentice-Hall, Englewood Cliffs, New Jersey, 1961.Google Scholar
  3. Paul R. HalmosMeasure TheoryVan Nostrand, Princeton, 1950; Springer-Verlag, Berlin and New York, 1974.Google Scholar
  4. Felix HausdorffSet Theory(J. Aumman et al.,translators), Chelsea, New York, 1957.Google Scholar
  5. Stanislaw SaksTheory of the Integral(L. C. Young, translator), Stechert-Hafner, New York, 1937.Google Scholar

Copyright information

© Springer Science+Business Media New York 1997

Authors and Affiliations

  • Yuan Shih Chow
    • 1
  • Henry Teicher
    • 2
  1. 1.Department of StatisticsColumbia UniversityNew YorkUSA
  2. 2.Department of StatisticsRutgers UniversityNew BrunswickUSA

Personalised recommendations