The First Mean Value Theorem for Integrals
Keiko Narita ; Noboru Endou ; Yasunari Shidama
Formalized Mathematics, Tome 16 (2008), p. 51-55 / Harvested from The Polish Digital Mathematics Library
Access to full text
Full (PDF)

In this article, we prove the first mean value theorem for integrals [16]. The formalization of various theorems about the properties of the Lebesgue integral is also presented.MML identifier: MESFUNC7, version: 7.8.09 4.97.1001

Publié le : 2008-01-01
EUDML-ID : urn:eudml:doc:267055 
@article{bwmeta1.element.doi-10_2478_v10037-008-0008-0,
     author = {Keiko Narita and Noboru Endou and Yasunari Shidama},
     title = {The First Mean Value Theorem for Integrals},
     journal = {Formalized Mathematics},
     volume = {16},
     year = {2008},
     pages = {51-55},
     zbl = {1321.46022},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_v10037-008-0008-0}
}

Keiko Narita; Noboru Endou; Yasunari Shidama. The First Mean Value Theorem for Integrals. Formalized Mathematics, Tome 16 (2008) pp. 51-55. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_v10037-008-0008-0/

[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] Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences. Formalized Mathematics, 1(1):107-114, 1990.

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

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

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

[7] Józef Białas. Some properties of the intervals. Formalized Mathematics, 5(1):21-26, 1996.

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

[9] Czesław Byliński. Finite sequences and tuples of elements of a non-empty sets. Formalized Mathematics, 1(3):529-536, 1990.

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

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

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

[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] Krzysztof Hryniewiecki. Basic properties of real numbers. Formalized Mathematics, 1(1):35-40, 1990.

[18] Rafał Kwiatek. Factorial and Newton coefficients. Formalized Mathematics, 1(5):887-890, 1990.

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

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

[21] Edmund Woronowicz. Relations and their basic properties. Formalized Mathematics, 1(1):73-83, 1990.

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