Advertisement

Abstract

In this chapter, we discuss the basics in the classical probability theory. Probability theory is based on measure theory, so that we start by reviewing measure theory.

Keywords

Measurable Function Probability Space Conditional Expectation Measure Theory Commutative Algebra 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. 9.
    Accardi, L.: Quantum Probability and Applications II: Proceedings Workshop Held Heidelberg. Springer, Berlin (1985) Google Scholar
  2. 34.
    Accardi, L., Lu, Y.G., Volovich, I.V.: Quantum Theory and Its Stochastic Limit. Springer, Berlin (2002) Google Scholar
  3. 207.
    Doob, J.L.: Stochastic Processes. Wiley, New York (1953) Google Scholar
  4. 234.
    Feller, W.: An Introduction to Probability Theory and Its Applications, vol. I. Wiley, New York (1950) Google Scholar
  5. 280.
    Gelfand, I.M., Vilenkin, N.Ya.: Generalized Functions. Applications of Harmonic Analysis. Academic Press, San Diego (1977) Google Scholar
  6. 335.
    Hida, T.: Brownian Motion. Springer, Berlin (1980) Google Scholar
  7. 355.
    Ihara, S.: Stochastic Process and Entropy. Iwanami, Tokyo (1984) (in Japanese) Google Scholar
  8. 378.
    Ito, K.: Probability Theory, vols. I, II, III. Iwanami, Tokyo (1976–1978) (in Japanese) Google Scholar
  9. 405.
    Khrennikov, A.: Interpretations of Probability. Frontiers in Probability Theory. De Gruyter, Berlin (1999) Google Scholar
  10. 438.
    Kolmogorov, A.N.: Grundbegriffe der Wahrscheinlichkeitsrechnung, Erg. Mat., 1933. Springer, Berlin (1977) Google Scholar
  11. 457.
    Kunisawa, K.: Probability Theory and Its Applications. Iwanami, Tokyo (1982) (in Japanese) Google Scholar
  12. 478.
    Levy, P.: Processus Stochastiques et Mouvement Brownien. Gauthier-Villars, Paris (1948) Google Scholar
  13. 479.
    Levy, P.: Problems Concrets d’Analyse Fonctionnelle. Gauthier-Villars, Paris (1951) Google Scholar
  14. 546.
    Neveu, J.: Bases Mathematiques du Calcul des Probabilites. Masson, Paris (1970) Google Scholar
  15. 631.
    Parthasarathy, K.R.: Probability Measure on Metric Spaces. Academic Press, San Diego (1967) Google Scholar
  16. 658.
    Prokhorov, Yu.V., Rozanov, Yu.A.: Probability Theory. Nauka, Moscow (1973) Google Scholar
  17. 766.
    Umegaki, H., Ohya, M.: Probabilistic Entropy. Kyoritsu, Tokyo (1983) (in Japanese) Google Scholar
  18. 768.
    Umegaki, H., Tsukada, M., Ohya, M.: Measure, Integral and Probability. Kyoritsu, Tokyo (1987) (in Japanese) Google Scholar

Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  1. 1.Information SciencesTokyo University of ScienceNodaJapan
  2. 2.Mathematical PhysicsSteklov Mathematical InstituteMoscowRussia

Personalised recommendations