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Riemann Integral of Functions from R into Real Normed Space Cover

Riemann Integral of Functions from R into Real Normed Space

Formalized Mathematics
Volume 19 (2011): Issue 1 (March 2011)
By: ,   and    
Open Access
|Jul 2011
References

References

  1. [1] Grzegorz Bancerek. The fundamental properties of natural numbers., 1():41-46, 1990.
    Search in Google Scholar
  2. [2] Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences., 1():107-114, 1990.
    Search in Google Scholar
  3. [3] Czesław Byliński. Finite sequences and tuples of elements of a non-empty sets., 1():529-536, 1990.
    Search in Google Scholar
  4. [4] Czesław Byliński. Functions and their basic properties., 1():55-65, 1990.
    Search in Google Scholar
  5. [5] Czesław Byliński. Functions from a set to a set., 1():153-164, 1990.
    Search in Google Scholar
  6. [6] Czesław Byliński. Partial functions., 1():357-367, 1990.
    Search in Google Scholar
  7. [7] Noboru Endou and Artur Korniłowicz. The definition of the Riemann definite integral and some related lemmas., 8():93-102, 1999.
    Search in Google Scholar
  8. [8] Noboru Endou, Katsumi Wasaki, and Yasunari Shidama. Darboux's theorem., 9():197-200, 2001.
    Search in Google Scholar
  9. [9] Noboru Endou, Katsumi Wasaki, and Yasunari Shidama. Definition of integrability for partial functions from R to R and integrability for continuous functions., 9():281-284, 2001.
    Search in Google Scholar
  10. [10] Noboru Endou, Katsumi Wasaki, and Yasunari Shidama. Scalar multiple of Riemann definite integral., 9():191-196, 2001.
    Search in Google Scholar
  11. [11] Krzysztof Hryniewiecki. Basic properties of real numbers., 1():35-40, 1990.
    Search in Google Scholar
  12. [12] Jarosław Kotowicz. Convergent sequences and the limit of sequences., 1():273-275, 1990.
    Search in Google Scholar
  13. [13] Beata Padlewska and Agata Darmochwał. Topological spaces and continuous functions., 1():223-230, 1990.
    Search in Google Scholar
  14. [14] Jan Popiołek. Real normed space., 2():111-115, 1991.
    Search in Google Scholar
  15. [15] Konrad Raczkowski and Paweł Sadowski. Topological properties of subsets in real numbers., 1():777-780, 1990.
    Search in Google Scholar
  16. [16] Murray R. Spiegel.. McGraw-Hill, 1974.
    Search in Google Scholar
  17. [17] Wojciech A. Trybulec. Vectors in real linear space., 1():291-296, 1990.
    Search in Google Scholar
  18. [18] Zinaida Trybulec. Properties of subsets., 1():67-71, 1990.
    Search in Google Scholar
  19. [19] Edmund Woronowicz. Relations defined on sets., 1():181-186, 1990.
    Search in Google Scholar
  20. [20] Hiroshi Yamazaki and Yasunari Shidama. Algebra of vector functions., 3():171-175, 1992.
    Search in Google Scholar
DOI: https://doi.org/10.2478/v10037-011-0003-8 | Journal eISSN: 1898-9934 | Journal ISSN: 1426-2630
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Language: English
Page range: 17 - 22
Published on: Jul 18, 2011
Published by: University of Białystok
In partnership with: Paradigm Publishing Services
Related subjects:
Computer sciences,
Artificial intelligence,
Computer sciences, other,
Mathematics,
Logic and set theory,
General mathematics

© 2011 Keiichi Miyajima, Takahiro Kato, Yasunari Shidama, published by University of Białystok
This work is licensed under the Creative Commons License.

Volume 19 (2011): Issue 1 (March 2011)
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