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