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Definition and some Properties of Information Entropy Cover

Definition and some Properties of Information Entropy

Formalized Mathematics
Volume 15 (2007): Issue 3 (September 2007)
By:  and    
Open Access
|Jun 2008
References

References

  1. [1] Grzegorz Bancerek. The ordinal numbers., 1(1):91-96, 1990.
    Search in Google Scholar
  2. [2] Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences., 1(1):107-114, 1990.
    Search in Google Scholar
  3. [3] P. Billingsley.. John Wiley & Sons, 1964.
    Search in Google Scholar
  4. [4] Czesław Byliński. Binary operations., 1(1):175-180, 1990.
    Search in Google Scholar
  5. [5] Czesław Byliński. Finite sequences and tuples of elements of a non-empty sets., 1(3):529-536, 1990.
    Search in Google Scholar
  6. [6] Czesław Byliński. Functions and their basic properties., 1(1):55-65, 1990.
    Search in Google Scholar
  7. [7] Czesław Byliński. Functions from a set to a set., 1(1):153-164, 1990.
    Search in Google Scholar
  8. [8] Czesław Byliński. Some basic properties of sets., 1(1):47-53, 1990.
    Search in Google Scholar
  9. [9] Czesław Byliński. The sum and product of finite sequences of real numbers., 1(4):661-668, 1990.
    Search in Google Scholar
  10. [10] Agata Darmochwał. The Euclidean space., 2(4):599-603, 1991.
    Search in Google Scholar
  11. [11] Shigeichi Hirasawa.. Baifukan CO., 1996.
    Search in Google Scholar
  12. [12] Katarzyna Jankowska. Matrices. Abelian group of matrices., 2(4):475-480, 1991.
    Search in Google Scholar
  13. [13] Artur Korniłowicz. On the real valued functions., 13(1):181-187, 2005.
    Search in Google Scholar
  14. [14] Jarosław Kotowicz. Real sequences and basic operations on them., 1(2):269-272, 1990.
    Search in Google Scholar
  15. [15] Rafał Kwiatek. Factorial and Newton coefficients., 1(5):887-890, 1990.
    Search in Google Scholar
  16. [16] Yatsuka Nakamura, Nobuyuki Tamaura, and Wenpai Chang. A theory of matrices of real elements., 14(1):21-28, 2006.
    Open DOISearch in Google Scholar
  17. [17] Library Committee of the Association of Mizar Users. Binary operations on numbers..
    Search in Google Scholar
  18. [18] Konrad Raczkowski and Andrzej Nedzusiak. Real exponents and logarithms., 2(2):213-216, 1991.
    Search in Google Scholar
  19. [19] Yasunari Shidama. The Taylor expansions., 12(2):195-200, 2004.
    Search in Google Scholar
  20. [20] Andrzej Trybulec. Subsets of complex numbers..
    Search in Google Scholar
  21. [21] Andrzej Trybulec. Tarski Grothendieck set theory., 1(1):9-11, 1990.
    Search in Google Scholar
  22. [22] Wojciech A. Trybulec. Vectors in real linear space., 1(2):291-296, 1990.
    Search in Google Scholar
  23. [23] Zinaida Trybulec. Properties of subsets., 1(1):67-71, 1990.
    Search in Google Scholar
  24. [24] Edmund Woronowicz. Relations and their basic properties., 1(1):73-83, 1990.
    Search in Google Scholar
  25. [25] Bo Zhang and Yatsuka Nakamura. The definition of finite sequences and matrices of probability, and addition of matrices of real elements., 14(3):101-108, 2006.
    Open DOISearch in Google Scholar
DOI: https://doi.org/10.2478/v10037-007-0012-9 | Journal eISSN: 1898-9934 | Journal ISSN: 1426-2630
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Language: English
Page range: 111 - 119
Published on: Jun 9, 2008
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

© 2008 Bo Zhang, Yatsuka Nakamura, published by University of Białystok
This work is licensed under the Creative Commons License.

Volume 15 (2007): Issue 3 (September 2007)
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