The Relevance of Measure and Probability, and Definition of Completeness of Probability

Bo Zhang; Hiroshi Yamazaki; Yatsuka Nakamura

Formalized Mathematics (2006)

  • Volume: 14, Issue: 4, page 225-229
  • ISSN: 1426-2630

Abstract

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In this article, we first discuss the relation between measure defined using extended real numbers and probability defined using real numbers. Further, we define completeness of probability, and its completion method, and also show that they coincide with those of measure.

How to cite

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Bo Zhang, Hiroshi Yamazaki, and Yatsuka Nakamura. "The Relevance of Measure and Probability, and Definition of Completeness of Probability." Formalized Mathematics 14.4 (2006): 225-229. <http://eudml.org/doc/266604>.

@article{BoZhang2006,
abstract = {In this article, we first discuss the relation between measure defined using extended real numbers and probability defined using real numbers. Further, we define completeness of probability, and its completion method, and also show that they coincide with those of measure.},
author = {Bo Zhang, Hiroshi Yamazaki, Yatsuka Nakamura},
journal = {Formalized Mathematics},
language = {eng},
number = {4},
pages = {225-229},
title = {The Relevance of Measure and Probability, and Definition of Completeness of Probability},
url = {http://eudml.org/doc/266604},
volume = {14},
year = {2006},
}

TY - JOUR
AU - Bo Zhang
AU - Hiroshi Yamazaki
AU - Yatsuka Nakamura
TI - The Relevance of Measure and Probability, and Definition of Completeness of Probability
JO - Formalized Mathematics
PY - 2006
VL - 14
IS - 4
SP - 225
EP - 229
AB - In this article, we first discuss the relation between measure defined using extended real numbers and probability defined using real numbers. Further, we define completeness of probability, and its completion method, and also show that they coincide with those of measure.
LA - eng
UR - http://eudml.org/doc/266604
ER -

References

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  1. [1] Grzegorz Bancerek. The fundamental properties of natural numbers. Formalized Mathematics, 1(1):41-46, 1990. Zbl06213858
  2. [2] Grzegorz Bancerek. Köonig's theorem. Formalized Mathematics, 1(3):589-593, 1990. 
  3. [3] Józef Białas. Completeness of the σ-additive measure. Measure theory. Formalized Mathematics, 2(5):689-693, 1991. 
  4. [4] Józef Białas. Infimum and supremum of the set of real numbers. Measure theory. Formalized Mathematics, 2(1):163-171, 1991. 
  5. [5] Józef Białas. Series of positive real numbers. Measure theory. Formalized Mathematics, 2(1):173-183, 1991. 
  6. [6] Józef Białas. The σ-additive measure theory. Formalized Mathematics, 2(2):263-270, 1991. 
  7. [7] Józef Białas. Some properties of the intervals. Formalized Mathematics, 5(1):21-26, 1996. 
  8. [8] Czesław Byliński. Functions and their basic properties. Formalized Mathematics, 1(1):55-65, 1990. 
  9. [9] Czesław Byliński. Functions from a set to a set. Formalized Mathematics, 1(1):153-164, 1990. 
  10. [10] Czesław Byliński. Some basic properties of sets. Formalized Mathematics, 1(1):47-53, 1990. 
  11. [11] Czesław Byliński and Piotr Rudnicki. Bounding boxes for compact sets in ε2. Formalized Mathematics, 6(3):427-440, 1997. 
  12. [12] Jarosław Kotowicz. Convergent sequences and the limit of sequences. Formalized Mathematics, 1(2):273-275, 1990. 
  13. [13] Andrzej Nędzusiak. Probability. Formalized Mathematics, 1(4):745-749, 1990. 
  14. [14] Andrzej Nędzusiak. σ-fields and probability. Formalized Mathematics, 1(2):401-407, 1990. 
  15. [15] Beata Padlewska. Families of sets. Formalized Mathematics, 1(1):147-152, 1990. 
  16. [16] Konrad Raczkowski and Andrzej Nędzusiak. Series. Formalized Mathematics, 2(4):449-452, 1991. 
  17. [17] Andrzej Trybulec. Subsets of complex numbers. To appear in Formalized Mathematics. 
  18. [18] Andrzej Trybulec. Tarski Grothendieck set theory. Formalized Mathematics, 1(1):9-11, 1990. 
  19. [19] Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990. 
  20. [20] Edmund Woronowicz. Relations and their basic properties. Formalized Mathematics, 1(1):73-83, 1990. 
  21. [21] Edmund Woronowicz. Relations defined on sets. Formalized Mathematics, 1(1):181-186, 1990. 
  22. [22] Bo Zhang, Hiroshi Yamazaki, and Yatsuka Nakamura. Inferior limit and superior limit of sequences of real numbers. Formalized Mathematics, 13(3):375-381, 2005. 
  23. [23] Bo Zhang, Hiroshi Yamazaki, and Yatsuka Nakamura. Set sequences and monotone class. Formalized Mathematics, 13(4):435-441, 2005. 

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