Fatou's Lemma and the Lebesgue's Convergence Theorem

Noboru Endou; Keiko Narita; Yasunari Shidama

Formalized Mathematics (2008)

  • Volume: 16, Issue: 4, page 305-309
  • ISSN: 1426-2630

Abstract

top
In this article we prove the Fatou's Lemma and Lebesgue's Convergence Theorem [10].MML identifier: MESFUN10, version: 7.9.01 4.101.1015

How to cite

top

Noboru Endou, Keiko Narita, and Yasunari Shidama. "Fatou's Lemma and the Lebesgue's Convergence Theorem." Formalized Mathematics 16.4 (2008): 305-309. <http://eudml.org/doc/267127>.

@article{NoboruEndou2008,
abstract = {In this article we prove the Fatou's Lemma and Lebesgue's Convergence Theorem [10].MML identifier: MESFUN10, version: 7.9.01 4.101.1015},
author = {Noboru Endou, Keiko Narita, Yasunari Shidama},
journal = {Formalized Mathematics},
keywords = {normed linear spaces; Banach spaces; duality and reflexivity; weak topologies; weak topologies},
language = {eng},
number = {4},
pages = {305-309},
title = {Fatou's Lemma and the Lebesgue's Convergence Theorem},
url = {http://eudml.org/doc/267127},
volume = {16},
year = {2008},
}

TY - JOUR
AU - Noboru Endou
AU - Keiko Narita
AU - Yasunari Shidama
TI - Fatou's Lemma and the Lebesgue's Convergence Theorem
JO - Formalized Mathematics
PY - 2008
VL - 16
IS - 4
SP - 305
EP - 309
AB - In this article we prove the Fatou's Lemma and Lebesgue's Convergence Theorem [10].MML identifier: MESFUN10, version: 7.9.01 4.101.1015
LA - eng
KW - normed linear spaces; Banach spaces; duality and reflexivity; weak topologies; weak topologies
UR - http://eudml.org/doc/267127
ER -

References

top
  1. [1] Grzegorz Bancerek. The ordinal numbers. Formalized Mathematics, 1(1):91-96, 1990. 
  2. [2] Józef Białas. Infimum and supremum of the set of real numbers. Measure theory. Formalized Mathematics, 2(1):163-171, 1991. 
  3. [3] Józef Białas. Series of positive real numbers. Measure theory. Formalized Mathematics, 2(1):173-183, 1991. 
  4. [4] Józef Białas. The σ-additive measure theory. Formalized Mathematics, 2(2):263-270, 1991. 
  5. [5] Czesław Byliński. Partial functions. Formalized Mathematics, 1(2):357-367, 1990. 
  6. [6] Noboru Endou and Yasunari Shidama. Integral of measurable function. Formalized Mathematics, 14(2):53-70, 2006. 
  7. [7] Noboru Endou, Yasunari Shidama, and Keiko Narita. Egoroff's theorem. Formalized Mathematics, 16(1):57-63, 2008. Zbl1298.46005
  8. [8] Noboru Endou, Katsumi Wasaki, and Yasunari Shidama. Basic properties of extended real numbers. Formalized Mathematics, 9(3):491-494, 2001. 
  9. [9] Noboru Endou, Katsumi Wasaki, and Yasunari Shidama. Definitions and basic properties of measurable functions. Formalized Mathematics, 9(3):495-500, 2001. 
  10. [10] P. R. Halmos. Measure Theory. Springer-Verlag, 1987. 
  11. [11] Jarosław Kotowicz. Monotone real sequences. Subsequences. Formalized Mathematics, 1(3):471-475, 1990. 
  12. [12] Andrzej Nedzusiak. σ-fields and probability. Formalized Mathematics, 1(2):401-407, 1990. 
  13. [13] Beata Perkowska. Functional sequence from a domain to a domain. Formalized Mathematics, 3(1):17-21, 1992. 
  14. [14] Andrzej Trybulec. Domains and their Cartesian products. Formalized Mathematics, 1(1):115-122, 1990. 
  15. [15] Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990. 
  16. [16] Edmund Woronowicz. Relations defined on sets. Formalized Mathematics, 1(1):181-186, 1990. 
  17. [17] 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. 

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.