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Classes of Sets, Measures, and Probability Spaces

  • Yuan Shih Chow
  • Henry Teicher
Chapter
  • 517 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 Ø. 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.

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References

  1. J. L. Doob, “Supplement,” Stochastic Processes, Wiley, New York, 1953.Google Scholar
  2. E. B. Dynkin, Theory of Markov Processes (D. E. Brown, translator), Prentice-Hall, Englewood Cliffs, New Jersey, 1961.Google Scholar
  3. Paul R. Halmos, Measure Theory, Van Nostrand, Princeton, 1950; Springer-Verlag, Berlin and New York, 1974.Google Scholar
  4. Felix Hausdorff, Set Theory (J. Aumman et al., translators), Chelsea, New York, 1957.zbMATHGoogle Scholar
  5. Stanislaw Saks, Theory of the Integral, (L. C. Young, translator), Stechert-Hafner, New York, 1937.Google Scholar

Copyright information

© Springer-Verlag New York Inc. 1988

Authors and Affiliations

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

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