Jump to ContentJump to Main Navigation
Show Summary Details
In This Section

Formalized Mathematics

(a computer assisted approach)

Editor-in-Chief: Matuszewski, Roman

4 Issues per year


SCImago Journal Rank (SJR) 2015: 0.134
Source Normalized Impact per Paper (SNIP) 2015: 0.686
Impact per Publication (IPP) 2015: 0.296

Open Access
Online
ISSN
1898-9934
See all formats and pricing
In This Section
Volume 17, Issue 2 (Jan 2009)

Issues

Probability on Finite Set and Real-Valued Random Variables

Hiroyuki Okazaki
  • Shinshu University, Nagano, Japan
/ Yasunari Shidama
  • Shinshu University, Nagano, Japan
Published Online: 2009-07-14 | DOI: https://doi.org/10.2478/v10037-009-0014-x

Probability on Finite Set and Real-Valued Random Variables

In the various branches of science, probability and randomness provide us with useful theoretical frameworks. The Formalized Mathematics has already published some articles concerning the probability: [23], [24], [25], and [30]. In order to apply those articles, we shall give some theorems concerning the probability and the real-valued random variables to prepare for further studies.

  • [1] Grzegorz Bancerek. Cardinal numbers. Formalized Mathematics, 1(2):377-382, 1990.

  • [2] Grzegorz Bancerek. The fundamental properties of natural numbers. Formalized Mathematics, 1(1):41-46, 1990.

  • [3] Grzegorz Bancerek. The ordinal numbers. Formalized Mathematics, 1(1):91-96, 1990.

  • [4] Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences. Formalized Mathematics, 1(1):107-114, 1990.

  • [5] Józef Białas. Infimum and supremum of the set of real numbers. Measure theory. Formalized Mathematics, 2(1):163-171, 1991.

  • [6] Józef Białas. Series of positive real numbers. Measure theory. Formalized Mathematics, 2(1):173-183, 1991.

  • [7] Józef Białas. The σ-additive measure theory. Formalized Mathematics, 2(2):263-270, 1991.

  • [8] Józef Białas. Some properties of the intervals. Formalized Mathematics, 5(1):21-26, 1996.

  • [9] Czesław Byliński. Functions and their basic properties. Formalized Mathematics, 1(1):55-65, 1990.

  • [10] Czesław Byliński. Functions from a set to a set. Formalized Mathematics, 1(1):153-164, 1990.

  • [11] Czesław Byliński. Partial functions. Formalized Mathematics, 1(2):357-367, 1990.

  • [12] Czesław Byliński. Some basic properties of sets. Formalized Mathematics, 1(1):47-53, 1990.

  • [13] Czesław Byliński. The sum and product of finite sequences of real numbers. Formalized Mathematics, 1(4):661-668, 1990.

  • [14] Agata Darmochwał. Finite sets. Formalized Mathematics, 1(1):165-167, 1990.

  • [15] Noboru Endou and Yasunari Shidama. Integral of measurable function. Formalized Mathematics, 14(2):53-70, 2006, doi:10.2478/v10037-006-0008-x. [Crossref]

  • [16] Noboru Endou, Katsumi Wasaki, and Yasunari Shidama. Basic properties of extended real numbers. Formalized Mathematics, 9(3):491-494, 2001.

  • [17] Noboru Endou, Katsumi Wasaki, and Yasunari Shidama. Definitions and basic properties of measurable functions. Formalized Mathematics, 9(3):495-500, 2001.

  • [18] Krzysztof Hryniewiecki. Basic properties of real numbers. Formalized Mathematics, 1(1):35-40, 1990.

  • [19] Grigory E. Ivanov. Definition of convex function and Jensen's inequality. Formalized Mathematics, 11(4):349-354, 2003.

  • [20] Jarosław Kotowicz. Real sequences and basic operations on them. Formalized Mathematics, 1(2):269-272, 1990.

  • [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.

  • [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. [Crossref]

  • [23] Andrzej Nędzusiak. Probability. Formalized Mathematics, 1(4):745-749, 1990.

  • [24] Andrzej Nędzusiak. σ-fields and probability. Formalized Mathematics, 1(2):401-407, 1990.

  • [25] Jan Popiołek. Introduction to probability. Formalized Mathematics, 1(4):755-760, 1990.

  • [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. [Crossref]

  • [27] Andrzej Trybulec. On the sets inhabited by numbers. Formalized Mathematics, 11(4):341-347, 2003.

  • [28] Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990.

  • [29] Edmund Woronowicz. Relations defined on sets. Formalized Mathematics, 1(1):181-186, 1990.

  • [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. [Crossref]

About the article


Published Online: 2009-07-14

Published in Print: 2009-01-01



Citation Information: Formalized Mathematics, ISSN (Online) 1898-9934, ISSN (Print) 1426-2630, DOI: https://doi.org/10.2478/v10037-009-0014-x. Export Citation

This content is open access.

Citing Articles

Here you can find all Crossref-listed publications in which this article is cited. If you would like to receive automatic email messages as soon as this article is cited in other publications, simply activate the “Citation Alert” on the top of this page.

[1]
Naeem Abbasi, Osman Hasan, and Sofiène Tahar
Electronic Proceedings in Theoretical Computer Science, 2013, Volume 122, Page 75
[2]
Hiroyuki Okazaki and Yasunari Shidama
Formalized Mathematics, 2010, Volume 18, Number 4

Comments (0)

Please log in or register to comment.
Log in