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Lebesgue's Convergence Theorem of Complex-Valued Function Cover

Lebesgue's Convergence Theorem of Complex-Valued Function

Open Access
|Jul 2009

References

  1. [1] Grzegorz Bancerek. The ordinal numbers. Formalized Mathematics, 1(1):91-96, 1990.
  2. [2] Józef Białas. Series of positive real numbers. Measure theory. Formalized Mathematics, 2(1):173-183, 1991.
  3. [3] Józef Białas. The σ-additive measure theory. Formalized Mathematics, 2(2):263-270, 1991.
  4. [4] Czesław Byliński. The complex numbers. Formalized Mathematics, 1(3):507-513, 1990.
  5. [5] Czesław Byliński. Functions and their basic properties. Formalized Mathematics, 1(1):55-65, 1990.
  6. [6] Czesław Byliński. Functions from a set to a set. Formalized Mathematics, 1(1):153-164, 1990.
  7. [7] Czesław Byliński. Partial functions. Formalized Mathematics, 1(2):357-367, 1990.
  8. [8] Noboru Endou, Keiko Narita, and Yasunari Shidama. The Lebesgue monotone convergence theorem. Formalized Mathematics, 16(2):167-175, 2008, doi:10.2478/v10037-008-0023-1.10.2478/v10037-008-0023-1
  9. [9] 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
  10. [10] 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
  11. [11] Noboru Endou, Katsumi Wasaki, and Yasunari Shidama. Definitions and basic properties of measurable functions. Formalized Mathematics, 9(3):495-500, 2001.
  12. [12] Krzysztof Hryniewiecki. Basic properties of real numbers. Formalized Mathematics, 1(1):35-40, 1990.
  13. [13] Jarosław Kotowicz. Convergent sequences and the limit of sequences. Formalized Mathematics, 1(2):273-275, 1990.
  14. [14] Jarosław Kotowicz. Real sequences and basic operations on them. Formalized Mathematics, 1(2):269-272, 1990.
  15. [15] 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
  16. [16] Keiko Narita, Noboru Endou, and Yasunari Shidama. The measurability of complex-valued functional sequences. Formalized Mathematics, 17(2):89-97, 2009, doi: 10.2478/v10037-009-0010-1.10.2478/v10037-009-0010-1
  17. [17] Adam Naumowicz. Conjugate sequences, bounded complex sequences and convergent complex sequences. Formalized Mathematics, 6(2):265-268, 1997.
  18. [18] Andrzej Nędzusiak. σ-fields and probability. Formalized Mathematics, 1(2):401-407, 1990.
  19. [19] Beata Padlewska. Families of sets. Formalized Mathematics, 1(1):147-152, 1990.
  20. [20] Beata Perkowska. Functional sequence from a domain to a domain. Formalized Mathematics, 3(1):17-21, 1992.
  21. [21] Konrad Raczkowski and Andrzej Nędzusiak. Series. Formalized Mathematics, 2(4):449-452, 1991.
  22. [22] 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
  23. [23] Yasunari Shidama and Artur Korniłowicz. Convergence and the limit of complex sequences. Series. Formalized Mathematics, 6(3):403-410, 1997.
  24. [24] Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990.
  25. [25] Edmund Woronowicz. Relations and their basic properties. Formalized Mathematics, 1(1):73-83, 1990.
  26. [26] Edmund Woronowicz. Relations defined on sets. Formalized Mathematics, 1(1):181-186, 1990.
DOI: https://doi.org/10.2478/v10037-009-0015-9 | Journal eISSN: 1898-9934 | Journal ISSN: 1426-2630
Language: English
Page range: 137 - 145
Published on: Jul 14, 2009
Published by: University of Białystok
In partnership with: Paradigm Publishing Services
Publication frequency: 1 issue per year

© 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)