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Integrability and the Integral of Partial Functions from R into R1 Cover

Integrability and the Integral of Partial Functions from R into R1

Formalized Mathematics
Volume 14 (2006): Issue 4 (December 2006)
By: Noboru Endou,  Yasunari Shidama and  Masahiko Yamazaki  
Open Access
|Jun 2008

References

  1. [1] Grzegorz Bancerek. The fundamental properties of natural numbers. Formalized Mathematics, 1(1):41-46, 1990.
    Search in Google Scholar
  2. [2] Grzegorz Bancerek. The ordinal numbers. Formalized Mathematics, 1(1):91-96, 1990.
    Search in Google Scholar
  3. [3] Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences. Formalized Mathematics, 1(1):107-114, 1990.
    Search in Google Scholar
  4. [4] Czesław Byliński. The complex numbers. Formalized Mathematics, 1(3):507-513, 1990.
    Search in Google Scholar
  5. [5] Czesław Byliński. Functions and their basic properties. Formalized Mathematics, 1(1):55-65, 1990.
    Search in Google Scholar
  6. [6] Czesław Byliński. Functions from a set to a set. Formalized Mathematics, 1(1):153-164, 1990.
    Search in Google Scholar
  7. [7] Czesław Byliński. Partial functions. Formalized Mathematics, 1(2):357-367, 1990.
    Search in Google Scholar
  8. [8] Czesław Byliński. The sum and product of finite sequences of real numbers. Formalized Mathematics, 1(4):661-668, 1990.
    Search in Google Scholar
  9. [9] Czesław Byliński and Piotr Rudnicki. Bounding boxes for compact sets in ε2. Formalized Mathematics, 6(3):427-440, 1997.
    Search in Google Scholar
  10. [10] Noboru Endou and Artur Korniłowicz. The definition of the Riemann definite integral and some related lemmas. Formalized Mathematics, 8(1):93-102, 1999.
    Search in Google Scholar
  11. [11] Noboru Endou, Katsumi Wasaki, and Yasunari Shidama. Definition of integrability for partial functions from R to R and integrability for continuous functions. Formalized Mathematics, 9(2):281-284, 2001.
    Search in Google Scholar
  12. [12] Noboru Endou, Katsumi Wasaki, and Yasunari Shidama. Integrability of bounded total functions. Formalized Mathematics, 9(2):271-274, 2001.
    Search in Google Scholar
  13. [13] Noboru Endou, Katsumi Wasaki, and Yasunari Shidama. Scalar multiple of Riemann definite integral. Formalized Mathematics, 9(1):191-196, 2001.
    Search in Google Scholar
  14. [14] Krzysztof Hryniewiecki. Basic properties of real numbers. Formalized Mathematics, 1(1):35-40, 1990.
    Search in Google Scholar
  15. [15] Jarosław Kotowicz. Convergent sequences and the limit of sequences. Formalized Mathematics, 1(2):273-275, 1990.
    Search in Google Scholar
  16. [16] Jarosław Kotowicz. Partial functions from a domain to the set of real numbers. Formalized Mathematics, 1(4):703-709, 1990.
    Search in Google Scholar
  17. [17] Jarosław Kotowicz. Real sequences and basic operations on them. Formalized Mathematics, 1(2):269-272, 1990.
    Search in Google Scholar
  18. [18] Jarosław Kotowicz and Yatsuka Nakamura. Introduction to Go-board - part I. Formalized Mathematics, 3(1):107-115, 1992.
    Search in Google Scholar
  19. [19] Konrad Raczkowski and Paweł Sadowski. Real function continuity. Formalized Mathematics, 1(4):787-791, 1990.
    Search in Google Scholar
  20. [20] Konrad Raczkowski and Paweł Sadowski. Real function differentiability. Formalized Mathematics, 1(4):797-801, 1990.
    Search in Google Scholar
  21. [21] Konrad Raczkowski and Paweł Sadowski. Topological properties of subsets in real numbers. Formalized Mathematics, 1(4):777-780, 1990.
    Search in Google Scholar
  22. [22] Andrzej Trybulec. Subsets of complex numbers. To appear in Formalized Mathematics.
    Search in Google Scholar
  23. [23] Andrzej Trybulec. Tarski Grothendieck set theory. Formalized Mathematics, 1(1):9-11, 1990.
    Search in Google Scholar
  24. [24] Michał J. Trybulec. Integers. Formalized Mathematics, 1(3):501-505, 1990.
    Search in Google Scholar
  25. [25] Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990.
    Search in Google Scholar
  26. [26] Edmund Woronowicz. Relations and their basic properties. Formalized Mathematics, 1(1):73-83, 1990.
    Search in Google Scholar
  27. [27] Edmund Woronowicz. Relations defined on sets. Formalized Mathematics, 1(1):181-186, 1990.
    Search in Google Scholar
DOI: https://doi.org/10.2478/v10037-006-0023-y | Journal eISSN: 1898-9934 | Journal ISSN: 1426-2630
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Language: English
Page range: 207 - 212
Published on: Jun 13, 2008
Published by: University of Białystok
In partnership with: Paradigm Publishing Services
Publication frequency: 1 issue per year
Related subjects:
Mathematics,
General mathematics,
Computer sciences,
Computer sciences, other

© 2008 Noboru Endou, Yasunari Shidama, Masahiko Yamazaki, published by University of Białystok
This work is licensed under the Creative Commons License.

Volume 14 (2006): Issue 4 (December 2006)