Have a personal or library account? Click to login
Probability on Finite Set and Real-Valued Random Variables Cover

Probability on Finite Set and Real-Valued Random Variables

Formalized Mathematics
Volume 17 (2009): Issue 2 (June 2009)
By: Hiroyuki Okazaki and  Yasunari Shidama  
Open Access
|Jul 2009

References

  1. [1] Grzegorz Bancerek. Cardinal numbers. Formalized Mathematics, 1(2):377-382, 1990.
    Search in Google Scholar
  2. [2] Grzegorz Bancerek. The fundamental properties of natural numbers. Formalized Mathematics, 1(1):41-46, 1990.
    Search in Google Scholar
  3. [3] Grzegorz Bancerek. The ordinal numbers. Formalized Mathematics, 1(1):91-96, 1990.
    Search in Google Scholar
  4. [4] Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences. Formalized Mathematics, 1(1):107-114, 1990.
    Search in Google Scholar
  5. [5] Józef Białas. Infimum and supremum of the set of real numbers. Measure theory. Formalized Mathematics, 2(1):163-171, 1991.
    Search in Google Scholar
  6. [6] Józef Białas. Series of positive real numbers. Measure theory. Formalized Mathematics, 2(1):173-183, 1991.
    Search in Google Scholar
  7. [7] Józef Białas. The σ-additive measure theory. Formalized Mathematics, 2(2):263-270, 1991.
    Search in Google Scholar
  8. [8] Józef Białas. Some properties of the intervals. Formalized Mathematics, 5(1):21-26, 1996.
    Search in Google Scholar
  9. [9] Czesław Byliński. Functions and their basic properties. Formalized Mathematics, 1(1):55-65, 1990.
    Search in Google Scholar
  10. [10] Czesław Byliński. Functions from a set to a set. Formalized Mathematics, 1(1):153-164, 1990.
    Search in Google Scholar
  11. [11] Czesław Byliński. Partial functions. Formalized Mathematics, 1(2):357-367, 1990.
    Search in Google Scholar
  12. [12] Czesław Byliński. Some basic properties of sets. Formalized Mathematics, 1(1):47-53, 1990.
    Search in Google Scholar
  13. [13] Czesław Byliński. The sum and product of finite sequences of real numbers. Formalized Mathematics, 1(4):661-668, 1990.
    Search in Google Scholar
  14. [14] Agata Darmochwał. Finite sets. Formalized Mathematics, 1(1):165-167, 1990.
    Search in Google Scholar
  15. [15] Noboru Endou and Yasunari Shidama. Integral of measurable function. Formalized Mathematics, 14(2):53-70, 2006, doi:10.2478/v10037-006-0008-x.10.2478/v10037-006-0008-x
    Search in Google Scholar
  16. [16] Noboru Endou, Katsumi Wasaki, and Yasunari Shidama. Basic properties of extended real numbers. Formalized Mathematics, 9(3):491-494, 2001.
    Search in Google Scholar
  17. [17] Noboru Endou, Katsumi Wasaki, and Yasunari Shidama. Definitions and basic properties of measurable functions. Formalized Mathematics, 9(3):495-500, 2001.
    Search in Google Scholar
  18. [18] Krzysztof Hryniewiecki. Basic properties of real numbers. Formalized Mathematics, 1(1):35-40, 1990.
    Search in Google Scholar
  19. [19] Grigory E. Ivanov. Definition of convex function and Jensen's inequality. Formalized Mathematics, 11(4):349-354, 2003.
    Search in Google Scholar
  20. [20] Jarosław Kotowicz. Real sequences and basic operations on them. Formalized Mathematics, 1(2):269-272, 1990.
    Search in Google Scholar
  21. [21] Jarosław Kotowicz and Yuji Sakai. Properties of partial functions from a domain to the set of real numbers. Formalized Mathematics, 3(2):279-288, 1992.
    Search in Google Scholar
  22. [22] Keiko Narita, Noboru Endou, and Yasunari Shidama. Integral of complex-valued measurable function. Formalized Mathematics, 16(4):319-324, 2008, doi:10.2478/v10037-008-0039-6.10.2478/v10037-008-0039-6
    Search in Google Scholar
  23. [23] Andrzej Nędzusiak. Probability. Formalized Mathematics, 1(4):745-749, 1990.
    Search in Google Scholar
  24. [24] Andrzej Nędzusiak. σ-fields and probability. Formalized Mathematics, 1(2):401-407, 1990.
    Search in Google Scholar
  25. [25] Jan Popiołek. Introduction to probability. Formalized Mathematics, 1(4):755-760, 1990.
    Search in Google Scholar
  26. [26] Yasunari Shidama and Noboru Endou. Integral of real-valued measurable function. Formalized Mathematics, 14(4):143-152, 2006, doi:10.2478/v10037-006-0018-8.10.2478/v10037-006-0018-8
    Search in Google Scholar
  27. [27] Andrzej Trybulec. On the sets inhabited by numbers. Formalized Mathematics, 11(4):341-347, 2003.
    Search in Google Scholar
  28. [28] Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990.
    Search in Google Scholar
  29. [29] Edmund Woronowicz. Relations defined on sets. Formalized Mathematics, 1(1):181-186, 1990.
    Search in Google Scholar
  30. [30] Bo Zhang, Hiroshi Yamazaki, and Yatsuka Nakamura. The relevance of measure and probability, and definition of completeness of probability. Formalized Mathematics, 14(4):225-229, 2006, doi:10.2478/v10037-006-0026-8.10.2478/v10037-006-0026-8
    Search in Google Scholar
DOI: https://doi.org/10.2478/v10037-009-0014-x | Journal eISSN: 1898-9934 | Journal ISSN: 1426-2630
Journal RSS Feed
Language: English
Page range: 129 - 136
Published on: Jul 14, 2009
Published by: University of Białystok
In partnership with: Paradigm Publishing Services
Publication frequency: 1 issue per year
Related subjects:
Computer sciences,
Computer sciences, other,
Mathematics,
General mathematics

© 2009 Hiroyuki Okazaki, Yasunari Shidama, published by University of Białystok
This work is licensed under the Creative Commons License.

Volume 17 (2009): Issue 2 (June 2009)