Have a personal or library account? Click to login
The Measurability of Complex-Valued Functional Sequences Cover

The Measurability of Complex-Valued Functional Sequences

Formalized Mathematics
Volume 17 (2009): Issue 2 (June 2009)
By: Keiko Narita,  Noboru Endou and  Yasunari Shidama  
Open Access
|Jul 2009

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] Józef Białas. Infimum and supremum of the set of real numbers. Measure theory. Formalized Mathematics, 2(1):163-171, 1991.
    Search in Google Scholar
  5. [5] Józef Białas. Series of positive real numbers. Measure theory. Formalized Mathematics, 2(1):173-183, 1991.
    Search in Google Scholar
  6. [6] Józef Białas. The σ-additive measure theory. Formalized Mathematics, 2(2):263-270, 1991.
    Search in Google Scholar
  7. [7] Józef Białas. Some properties of the intervals. Formalized Mathematics, 5(1):21-26, 1996.
    Search in Google Scholar
  8. [8] Czesław Byliński. The complex numbers. Formalized Mathematics, 1(3):507-513, 1990.
    Search in Google Scholar
  9. [9] Czesław Byliński. Functions and their basic properties. Formalized Mathematics, 1(1):55-65, 1990.
    Search in Google Scholar
  10. [10] Czesław Byliński. Functions from a set to a set. Formalized Mathematics, 1(1):153-164, 1990.
    Search in Google Scholar
  11. [11] Czesław Byliński. Partial functions. Formalized Mathematics, 1(2):357-367, 1990.
    Search in Google Scholar
  12. [12] Czesław Byliński. Some basic properties of sets. Formalized Mathematics, 1(1):47-53, 1990.
    Search in Google Scholar
  13. [13] Wenpai Chang, Hiroshi Yamazaki, and Yatsuka Nakamura. The inner product and conjugate of finite sequences of complex numbers. Formalized Mathematics, 13(3):367-373, 2005.
    Search in Google Scholar
  14. [14] Noboru Endou and Yasunari Shidama. Integral of measurable function. Formalized Mathematics, 14(2):53-70, 2006, doi:10.2478/v10037-006-0008-x.10.2478/v10037-006-0008-x
    Search in Google Scholar
  15. [15] Noboru Endou, Yasunari Shidama, and Keiko Narita. Egoroff's theorem. Formalized Mathematics, 16(1):57-63, 2008, doi:10.2478/v10037-008-0009-z.10.2478/v10037-008-0009-z
    Search in Google Scholar
  16. [16] 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
  17. [17] Jarosław Kotowicz. Convergent sequences and the limit of sequences. Formalized Mathematics, 1(2):273-275, 1990.
    Search in Google Scholar
  18. [18] Jarosław Kotowicz and Yuji Sakai. Properties of partial functions from a domain to the set of real numbers. Formalized Mathematics, 3(2):279-288, 1992.
    Search in Google Scholar
  19. [19] Keiko Narita, Noboru Endou, and Yasunari Shidama. Integral of complex-valued measurable function. Formalized Mathematics, 16(4):319-324, 2008, doi:10.2478/v10037-008-0039-6.10.2478/v10037-008-0039-6
    Search in Google Scholar
  20. [20] Adam Naumowicz. Conjugate sequences, bounded complex sequences and convergent complex sequences. Formalized Mathematics, 6(2):265-268, 1997.
    Search in Google Scholar
  21. [21] Andrzej Nędzusiak. σ-fields and probability. Formalized Mathematics, 1(2):401-407, 1990.
    Search in Google Scholar
  22. [22] Beata Padlewska. Families of sets. Formalized Mathematics, 1(1):147-152, 1990.
    Search in Google Scholar
  23. [23] Beata Perkowska. Functional sequence from a domain to a domain. Formalized Mathematics, 3(1):17-21, 1992.
    Search in Google Scholar
  24. [24] Yasunari Shidama and Noboru Endou. Integral of real-valued measurable function. Formalized Mathematics, 14(4):143-152, 2006, doi:10.2478/v10037-006-0018-8.10.2478/v10037-006-0018-8
    Search in Google Scholar
  25. [25] Yasunari Shidama and Artur Korniłowicz. Convergence and the limit of complex sequences. Series. Formalized Mathematics, 6(3):403-410, 1997.
    Search in Google Scholar
  26. [26] Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990.
    Search in Google Scholar
  27. [27] Edmund Woronowicz. Relations and their basic properties. Formalized Mathematics, 1(1):73-83, 1990.
    Search in Google Scholar
  28. [28] Hiroshi Yamazaki, Noboru Endou, Yasunari Shidama, and Hiroyuki Okazaki. Inferior limit, superior limit and convergence of sequences of extended real numbers. Formalized Mathematics, 15(4):231-236, 2007, doi:10.2478/v10037-007-0026-3.10.2478/v10037-007-0026-3
    Search in Google Scholar
DOI: https://doi.org/10.2478/v10037-009-0010-1 | Journal eISSN: 1898-9934 | Journal ISSN: 1426-2630
Journal RSS Feed
Language: English
Page range: 89 - 97
Published on: Jul 14, 2009
Published by: University of Białystok
In partnership with: Paradigm Publishing Services
Publication frequency: 1 issue per year
Related subjects:
Computer sciences,
Computer sciences, other,
Mathematics,
General mathematics

© 2009 Keiko Narita, Noboru Endou, Yasunari Shidama, published by University of Białystok
This work is licensed under the Creative Commons License.

Volume 17 (2009): Issue 2 (June 2009)