The Lebesgue Monotone Convergence Theorem

Noboru Endou; Keiko Narita; Yasunari Shidama

Formalized Mathematics (2008)

  • Volume: 16, Issue: 2, page 167-175
  • ISSN: 1426-2630

Abstract

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In this article we prove the Monotone Convergence Theorem [16].MML identifier: MESFUNC9, version: 7.8.10 4.100.1011

How to cite

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Noboru Endou, Keiko Narita, and Yasunari Shidama. "The Lebesgue Monotone Convergence Theorem." Formalized Mathematics 16.2 (2008): 167-175. <http://eudml.org/doc/267197>.

@article{NoboruEndou2008,
abstract = {In this article we prove the Monotone Convergence Theorem [16].MML identifier: MESFUNC9, version: 7.8.10 4.100.1011},
author = {Noboru Endou, Keiko Narita, Yasunari Shidama},
journal = {Formalized Mathematics},
keywords = {normed linear spaces; Banach spaces; duality; orthogonal projection; Riesz representation},
language = {eng},
number = {2},
pages = {167-175},
title = {The Lebesgue Monotone Convergence Theorem},
url = {http://eudml.org/doc/267197},
volume = {16},
year = {2008},
}

TY - JOUR
AU - Noboru Endou
AU - Keiko Narita
AU - Yasunari Shidama
TI - The Lebesgue Monotone Convergence Theorem
JO - Formalized Mathematics
PY - 2008
VL - 16
IS - 2
SP - 167
EP - 175
AB - In this article we prove the Monotone Convergence Theorem [16].MML identifier: MESFUNC9, version: 7.8.10 4.100.1011
LA - eng
KW - normed linear spaces; Banach spaces; duality; orthogonal projection; Riesz representation
UR - http://eudml.org/doc/267197
ER -

References

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  4. [4] Józef Białas. Series of positive real numbers. Measure theory. Formalized Mathematics, 2(1):173-183, 1991. 
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  6. [6] Czesław Byliński. Binary operations. Formalized Mathematics, 1(1):175-180, 1990. 
  7. [7] Czesław Byliński. Functions and their basic properties. Formalized Mathematics, 1(1):55-65, 1990. 
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  11. [11] Noboru Endou and Yasunari Shidama. Integral of measurable function. Formalized Mathematics, 14(2):53-70, 2006. 
  12. [12] Noboru Endou, Yasunari Shidama, and Keiko Narita. Egoroff's theorem. Formalized Mathematics, 16(1):57-63, 2008. Zbl1298.46005
  13. [13] Noboru Endou, Katsumi Wasaki, and Yasunari Shidama. Basic properties of extended real numbers. Formalized Mathematics, 9(3):491-494, 2001. 
  14. [14] Noboru Endou, Katsumi Wasaki, and Yasunari Shidama. Definitions and basic properties of measurable functions. Formalized Mathematics, 9(3):495-500, 2001. 
  15. [15] Noboru Endou, Katsumi Wasaki, and Yasunari Shidama. The measurability of extended real valued functions. Formalized Mathematics, 9(3):525-529, 2001. 
  16. [16] P. R. Halmos. Measure Theory. Springer-Verlag, 1987. 
  17. [17] Andrzej Nedzusiak. σ-fields and probability. Formalized Mathematics, 1(2):401-407, 1990. 
  18. [18] Beata Padlewska. Families of sets. Formalized Mathematics, 1(1):147-152, 1990. 
  19. [19] Beata Perkowska. Functional sequence from a domain to a domain. Formalized Mathematics, 3(1):17-21, 1992. 
  20. [20] Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990. 
  21. [21] Edmund Woronowicz. Relations defined on sets. Formalized Mathematics, 1(1):181-186, 1990. 
  22. [22] 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. 

Citations in EuDML Documents

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  1. Noboru Endou, Hiroyuki Okazaki, Yasunari Shidama, Double Sequences and Limits
  2. Noboru Endou, Hiroyuki Okazaki, Yasunari Shidama, Hopf Extension Theorem of Measure
  3. Noboru Endou, Double Series and Sums
  4. Keiko Narita, Noboru Endou, Yasunari Shidama, Lebesgue's Convergence Theorem of Complex-Valued Function
  5. Noboru Endou, Extended Real-Valued Double Sequence and Its Convergence
  6. Noboru Endou, Construction of Measure from Semialgebra of Sets1
  7. Noboru Endou, Product Pre-Measure

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