Skip to main content
Have a personal or library account? Click to login
Weak Convergence and Weak Convergence Cover

Weak Convergence and Weak Convergence

Formalized Mathematics
Volume 23 (2015): Issue 3 (September 2015)
By: ,   and    
Open Access
|Sep 2015
References

References

  1. [1] Grzegorz Bancerek. The fundamental properties of natural numbers., 1(1):41-46, 1990.
    Search in Google Scholar
  2. [2] Grzegorz Bancerek. The ordinal numbers., 1(1):91-96, 1990.
    Search in Google Scholar
  3. [3] Haim Brezis. Functional Analysis, Sobolev Spaces and Partial Differential Equations. Springer, 2011.
    Open DOISearch in Google Scholar
  4. [4] Czesław Bylinski. The complex numbers., 1(3):507-513, 1990.
    Search in Google Scholar
  5. [5] Czesław Bylinski. Functions and their basic properties., 1(1): 55-65, 1990.
    Search in Google Scholar
  6. [6] Czesław Bylinski. Functions from a set to a set., 1(1):153-164, 1990.
    Search in Google Scholar
  7. [7] Czesław Bylinski. Partial functions., 1(2):357-367, 1990.
    Search in Google Scholar
  8. [8] Czesław Bylinski. Some basic properties of sets., 1(1):47-53, 1990.
    Search in Google Scholar
  9. [9] Noboru Endou, Yasunari Shidama, and Katsumasa Okamura. Baire’s category theorem and some spaces generated from real normed space., 14(4): 213-219, 2006. doi:10.2478/v10037-006-0024-x.
    Open DOISearch in Google Scholar
  10. [10] Krzysztof Hryniewiecki. Recursive definitions., 1(2):321-328, 1990.
    Search in Google Scholar
  11. [11] Artur Korniłowicz. Recursive definitions. Part II., 12(2):167-172, 2004.
    Search in Google Scholar
  12. [12] Jarosław Kotowicz. Monotone real sequences. Subsequences., 1 (3):471-475, 1990.
    Search in Google Scholar
  13. [13] Jarosław Kotowicz. Real sequences and basic operations on them., 1(2):269-272, 1990.
    Search in Google Scholar
  14. [14] Jarosław Kotowicz. Convergent sequences and the limit of sequences., 1(2):273-275, 1990.
    Search in Google Scholar
  15. [15] Jarosław Kotowicz. Convergent real sequences. Upper and lower bound of sets of real numbers., 1(3):477-481, 1990.
    Search in Google Scholar
  16. [16] Kazuhisa Nakasho, Yuichi Futa, and Yasunari Shidama. Topological properties of real normed space., 22(3):209-223, 2014. doi:10.2478/forma-2014-0024.
    Open DOISearch in Google Scholar
  17. [17] Keiko Narita, Noboru Endou, and Yasunari Shidama. Dual spaces and Hahn-Banach theorem., 22(1):69-77, 2014. doi:10.2478/forma-2014-0007.
    Open DOISearch in Google Scholar
  18. [18] Keiko Narita, Noboru Endou, and Yasunari Shidama. Bidual spaces and reflexivity of real normed spaces., 22(4):303-311, 2014. doi:10.2478/forma-2014-0030.
    Open DOISearch in Google Scholar
  19. [19] Adam Naumowicz. Conjugate sequences, bounded complex sequences and convergent complex sequences., 6(2):265-268, 1997.
    Search in Google Scholar
  20. [20] Takaya Nishiyama, Keiji Ohkubo, and Yasunari Shidama. The continuous functions on normed linear spaces., 12(3):269-275, 2004.
    Search in Google Scholar
  21. [21] Bogdan Nowak and Andrzej Trybulec. Hahn-Banach theorem., 4(1):29-34, 1993.
    Search in Google Scholar
  22. [22] Jan Popiołek. Real normed space., 2(1):111-115, 1991.
    Search in Google Scholar
  23. [23] Michael Reed and Barry Simon. Methods of modern mathematical physics. Vol. 1. Academic Press, New York, 1972.
    Open DOISearch in Google Scholar
  24. [24] Walter Rudin. Functional Analysis. New York, McGraw-Hill, 2nd edition, 1991.
    Search in Google Scholar
  25. [25] Hideki Sakurai, Hisayoshi Kunimune, and Yasunari Shidama. Uniform boundedness principle., 16(1):19-21, 2008. doi:10.2478/v10037-008-0003-5.
    Open DOISearch in Google Scholar
  26. [26] Yasunari Shidama. Banach space of bounded linear operators., 12(1):39-48, 2004.
    Search in Google Scholar
  27. [27] Yasumasa Suzuki, Noboru Endou, and Yasunari Shidama. Banach space of absolute summable real sequences., 11(4):377-380, 2003.
    Search in Google Scholar
  28. [28] Andrzej Trybulec. Binary operations applied to functions., 1 (2):329-334, 1990.
    Search in Google Scholar
  29. [29] Andrzej Trybulec. On the sets inhabited by numbers., 11(4): 341-347, 2003.
    Search in Google Scholar
  30. [30] Michał J. Trybulec. Integers., 1(3):501-505, 1990.
    Search in Google Scholar
  31. [31] Wojciech A. Trybulec. Vectors in real linear space., 1(2):291-296, 1990.
    Search in Google Scholar
  32. [32] Wojciech A. Trybulec. Basis of real linear space., 1(5):847-850, 1990.
    Search in Google Scholar
  33. [33] Zinaida Trybulec. Properties of subsets., 1(1):67-71, 1990.
    Search in Google Scholar
  34. [34] Edmund Woronowicz. Relations and their basic properties., 1 (1):73-83, 1990.
    Search in Google Scholar
  35. [35] Edmund Woronowicz. Relations defined on sets., 1(1):181-186, 1990.
    Search in Google Scholar
  36. [36] Kosaku Yoshida. Functional Analysis. Springer, 1980.
    Search in Google Scholar
  37. [37] Bo Zhang, Hiroshi Yamazaki, and Yatsuka Nakamura. Inferior limit and superior limit of sequences of real numbers., 13(3):375-381, 2005.
    Search in Google Scholar
DOI: https://doi.org/10.1515/forma-2015-0019 | Journal eISSN: 1898-9934 | Journal ISSN: 1426-2630
Journal RSS Feed
Language: English
Page range: 231 - 241
Submitted on: Jul 1, 2015
Published on: Sep 30, 2015
Published by: University of Białystok
In partnership with: Paradigm Publishing Services
Keywords:
normed linear spaces,
Banach spaces,
duality and reflexivity,
weak topologies,
weak* topologies
MSC:
46E15,
46B10,
03B35
MML:
DUALSP03
Related subjects:
Computer sciences,
Artificial intelligence,
Computer sciences, other,
Mathematics,
Logic and set theory,
General mathematics

© 2015 Keiko Narita, Yasunari Shidama, Noboru Endou, published by University of Białystok
This work is licensed under the Creative Commons Attribution-ShareAlike 3.0 License.

Volume 23 (2015): Issue 3 (September 2015)
Previous article
Next article