The Lebesgue Monotone Convergence Theorem
Noboru Endou ; Keiko Narita ; Yasunari Shidama
Formalized Mathematics, Tome 16 (2008), p. 167-175 / Harvested from The Polish Digital Mathematics Library

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

Publié le : 2008-01-01
EUDML-ID : urn:eudml:doc:267197
@article{bwmeta1.element.doi-10_2478_v10037-008-0023-1,
     author = {Noboru Endou and Keiko Narita and Yasunari Shidama},
     title = {The Lebesgue Monotone Convergence Theorem},
     journal = {Formalized Mathematics},
     volume = {16},
     year = {2008},
     pages = {167-175},
     zbl = {1321.46022},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_v10037-008-0023-1}
}
Noboru Endou; Keiko Narita; Yasunari Shidama. The Lebesgue Monotone Convergence Theorem. Formalized Mathematics, Tome 16 (2008) pp. 167-175. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_v10037-008-0023-1/

[1] Grzegorz Bancerek. The fundamental properties of natural numbers. Formalized Mathematics, 1(1):41-46, 1990. | Zbl 06213858

[2] Grzegorz Bancerek. The ordinal numbers. Formalized Mathematics, 1(1):91-96, 1990.

[3] Józef Białas. Infimum and supremum of the set of real numbers. Measure theory. Formalized Mathematics, 2(1):163-171, 1991.

[4] Józef Białas. Series of positive real numbers. Measure theory. Formalized Mathematics, 2(1):173-183, 1991.

[5] Józef Białas. The σ-additive measure theory. Formalized Mathematics, 2(2):263-270, 1991.

[6] Czesław Byliński. Binary operations. Formalized Mathematics, 1(1):175-180, 1990.

[7] Czesław Byliński. Functions and their basic properties. Formalized Mathematics, 1(1):55-65, 1990.

[8] Czesław Byliński. Functions from a set to a set. Formalized Mathematics, 1(1):153-164, 1990.

[9] Czesław Byliński. Partial functions. Formalized Mathematics, 1(2):357-367, 1990.

[10] Czesław Byliński. Some basic properties of sets. Formalized Mathematics, 1(1):47-53, 1990.

[11] Noboru Endou and Yasunari Shidama. Integral of measurable function. Formalized Mathematics, 14(2):53-70, 2006.

[12] Noboru Endou, Yasunari Shidama, and Keiko Narita. Egoroff's theorem. Formalized Mathematics, 16(1):57-63, 2008. | Zbl 1298.46005

[13] Noboru Endou, Katsumi Wasaki, and Yasunari Shidama. Basic properties of extended real numbers. Formalized Mathematics, 9(3):491-494, 2001.

[14] Noboru Endou, Katsumi Wasaki, and Yasunari Shidama. Definitions and basic properties of measurable functions. Formalized Mathematics, 9(3):495-500, 2001.

[15] Noboru Endou, Katsumi Wasaki, and Yasunari Shidama. The measurability of extended real valued functions. Formalized Mathematics, 9(3):525-529, 2001.

[16] P. R. Halmos. Measure Theory. Springer-Verlag, 1987.

[17] Andrzej Nedzusiak. σ-fields and probability. Formalized Mathematics, 1(2):401-407, 1990.

[18] Beata Padlewska. Families of sets. Formalized Mathematics, 1(1):147-152, 1990.

[19] Beata Perkowska. Functional sequence from a domain to a domain. Formalized Mathematics, 3(1):17-21, 1992.

[20] Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990.

[21] Edmund Woronowicz. Relations defined on sets. Formalized Mathematics, 1(1):181-186, 1990.

[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.