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Inferior Limit, Superior Limit and Convergence of Sequences of Extended Real Numbers Cover

Inferior Limit, Superior Limit and Convergence of Sequences of Extended Real Numbers

Formalized Mathematics
Volume 15 (2007): Issue 4 (December 2007)
By: Hiroshi Yamazaki,  Noboru Endou,  Yasunari Shidama and  Hiroyuki Okazaki  
Open Access
|Jun 2008

References

  1. [4] Józef Białas. The σ-additive measure theory. Formalized Mathematics, 2(2):263-270, 1991.
    Search in Google Scholar
  2. [5] Czesław Byliński. Functions and their basic properties. Formalized Mathematics, 1(1):55-65, 1990.
    Search in Google Scholar
  3. [6] Czesław Byliński. Functions from a set to a set. Formalized Mathematics, 1(1):153-164, 1990.
    Search in Google Scholar
  4. [7] Czesław Byliński. Partial functions. Formalized Mathematics, 1(2):357-367, 1990.
    Search in Google Scholar
  5. [8] Czesław Byliński and Piotr Rudnicki. Bounding boxes for compact sets in ε2. Formalized Mathematics, 6(3):427-440, 1997.
    Search in Google Scholar
  6. [9] Noboru Endou and Yasunari Shidama. Integral of measurable function. Formalized Mathematics, 14(2):53-70, 2006.10.2478/v10037-006-0008-x
    Search in Google Scholar
  7. [10] Noboru Endou, Katsumi Wasaki, and Yasunari Shidama. Definitions and basic properties of measurable functions. Formalized Mathematics, 9(3):495-500, 2001.
    Search in Google Scholar
  8. [11] Adam Grabowski. On the Kuratowski limit operators. Formalized Mathematics, 11(4):399-409, 2003.
    Search in Google Scholar
  9. [12] Jarosław Kotowicz. Convergent real sequences. Upper and lower bound of sets of real numbers. Formalized Mathematics, 1(3):477-481, 1990.
    Search in Google Scholar
  10. [13] Jarosław Kotowicz. Convergent sequences and the limit of sequences. Formalized Mathematics, 1(2):273-275, 1990.
    Search in Google Scholar
  11. [14] Jarosław Kotowicz. Monotone real sequences. Subsequences. Formalized Mathematics, 1(3):471-475, 1990.
    Search in Google Scholar
  12. [15] Jarosław Kotowicz. Real sequences and basic operations on them. Formalized Mathematics, 1(2):269-272, 1990.
    Search in Google Scholar
  13. [16] Andrzej Nedzusiak. σ-fields and probability. Formalized Mathematics, 1(2):401-407, 1990.
    Search in Google Scholar
  14. [17] Andrzej Trybulec. Subsets of complex numbers. To appear in Formalized Mathematics.
    Search in Google Scholar
  15. [18] Andrzej Trybulec. Tarski Grothendieck set theory. Formalized Mathematics, 1(1):9-11, 1990.
    Search in Google Scholar
  16. [19] Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990.
    Search in Google Scholar
  17. [20] Edmund Woronowicz. Relations and their basic properties. Formalized Mathematics, 1(1):73-83, 1990.
    Search in Google Scholar
  18. [21] Edmund Woronowicz. Relations defined on sets. Formalized Mathematics, 1(1):181-186, 1990.
    Search in Google Scholar
  19. [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.
    Search in Google Scholar
  20. [1] Grzegorz Bancerek. The ordinal numbers. Formalized Mathematics, 1(1):91-96, 1990.
    Search in Google Scholar
  21. [2] Józef Białas. Infimum and supremum of the set of real numbers. Measure theory. Formalized Mathematics, 2(1):163-171, 1991.
    Search in Google Scholar
  22. [3] Józef Białas. Series of positive real numbers. Measure theory. Formalized Mathematics, 2(1):173-183, 1991.
    Search in Google Scholar
DOI: https://doi.org/10.2478/v10037-007-0026-3 | Journal eISSN: 1898-9934 | Journal ISSN: 1426-2630
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Language: English
Page range: 231 - 235
Published on: Jun 9, 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 Hiroshi Yamazaki, Noboru Endou, Yasunari Shidama, Hiroyuki Okazaki, published by University of Białystok
This work is licensed under the Creative Commons License.

Volume 15 (2007): Issue 4 (December 2007)