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Probability-1 pp 159-371 | Cite as

Mathematical Foundations of Probability Theory

  • Albert N. Shiryaev
Part of the Graduate Texts in Mathematics book series (GTM, volume 95)

Abstract

The theory of probability, as a mathematical discipline, can and should be developed from axioms in exactly the same way as Geometry and Algebra. This means that after we have defined the elements to be studied and their basic relations, and have stated the axioms by which these relations are to be governed, all further exposition must be based exclusively on these axioms, independent of the usual concrete meaning of these elements and their relations.

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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  • Albert N. Shiryaev
    • 1
  1. 1.Department of Probability Theory and Mathematical StatisticsSteklov Mathematical Institute and Lomonosov Moscow State UniversityMoscowRussia

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