## Integral of Measurable Function^{1}

In this paper we construct integral of measurable function.

Show Summary Details# Integral of Measurable Function^{1}

#### Open Access

## Integral of Measurable Function^{1}

## About the article

## Citing Articles

*Formalized Mathematics*, 2017, Volume 25, Number 3*Formalized Mathematics*, 2010, Volume 18, Number 3*Formalized Mathematics*, 2007, Volume 15, Number 4*Formalized Mathematics*, 2008, Volume 16, Number 2*Formalized Mathematics*, 2008, Volume 16, Number 1*Formalized Mathematics*, 2009, Volume 17, Number 2*Formalized Mathematics*, 2009, Volume 17, Number 2*Formalized Mathematics*, 2009, Volume 17, Number 2*Formalized Mathematics*, 2008, Volume 16, Number 4*Formalized Mathematics*, 2009, Volume 17, Number 2*Formalized Mathematics*, 2008, Volume 16, Number 4*Formalized Mathematics*, 2008, Volume 16, Number 1*Formalized Mathematics*, 2008, Volume 16, Number 4

More options …# Formalized Mathematics

### (a computer assisted approach)

More options …

Editor-in-Chief: Matuszewski, Roman

4 Issues per year

SCImago Journal Rank (SJR) 2016: 0.207

Source Normalized Impact per Paper (SNIP) 2016: 0.315

Noboru Endou / Yasunari Shidama

In this paper we construct integral of measurable function.

[1] Grzegorz Bancerek. The ordinal numbers.

*Formalized Mathematics*, 1(1):91-96, 1990.Google Scholar[2] Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences.

*Formalized Mathematics*, 1(1):107-114, 1990.Google Scholar[3] Józef Białas. Infimum and supremum of the set of real numbers. Measure theory.

*Formalized Mathematics*, 2(1):163-171, 1991.Google Scholar[4] Józef Białcs. Series of positive real numbers. Measure theory.

*Formalized Mathematics*, 2(1):173-183, 1991.Google Scholar[5] Józef Białas. The σ-additive measure theory.

*Formalized Mathematics*, 2(2):263-270, 1991.Google Scholar[6] Józef Białas. Some properties of the intervals.

*Formalized Mathematics*, 5(1):21-26, 1996.Google Scholar[7] Czesław Byliński. Basic functions and operations on functions.

*Formalized Mathematics*, 1(1):245-254, 1990.Google Scholar[8] Czesław Byliński. Binary operations applied to finite sequences.

*Formalized Mathematics*, 1(4):643-649, 1990.Google Scholar[9] Czesław Byliński. Functions and their basic properties.

*Formalized Mathematics*, 1(1):55-65, 1990.Google Scholar[10] Czesław Byliński. Functions from a set to a set.

*Formalized Mathematics*, 1(1):153-164, 1990.Google Scholar[11] Czesław Byliński. Partial functions.

*Formalized Mathematics*, 1(2):357-367, 1990.Google Scholar[12] Czesław Byliński. Some basic properties of sets.

*Formalized Mathematics*, 1(1):47-53, 1990.Google Scholar[13] Agata Darmochwał. Finite sets.

*Formalized Mathematics*, 1(1):165-167, 1990.Google Scholar[14] Noboru Endou, Katsumi Wasaki, and Yasunari Shidama. Basic properties of extended real numbers.

*Formalized Mathematics*, 9(3):491-494, 2001.Google Scholar[15] Noboru Endou, Katsumi Wasaki, and Yasunari Shidama. Definitions and basic properties of measurable functions.

*Formalized Mathematics*, 9(3):495-500, 2001.Google Scholar[16] Noboru Endou, Katsumi Wasaki, and Yasunari Shidama. The measurability of extended real valued functions.

*Formalized Mathematics*, 9(3):525-529, 2001.Google Scholar[17] Noboru Endou, Katsumi Wasaki, and Yasunari Shidama. Some properties of extended real numbers operations: abs, min and max.

*Formalized Mathematics*, 9(3):511-516, 2001.Google Scholar[18] Krzysztof Hryniewiecki. Basic properties of real numbers.

*Formalized Mathematics*, 1(1):35-40, 1990.Google Scholar[19] Grigory E. Ivanov. Definition of convex function and Jensen's inequality.

*Formalized Mathematics*, 11(4):349-354, 2003.Google Scholar[20] Andrzej Kondracki. Basic properties of rational numbers.

*Formalized Mathematics*, 1(5):841-845, 1990.Google Scholar[21] Jarosław Kotowicz and Yuji Sakai. Properties of partial functions from a domain to the set of real numbers.

*Formalized Mathematics*, 3(2):279-288, 1992.Google Scholar[22] Rafał Kwiatek. Factorial and Newton coefficients.

*Formalized Mathematics*, 1(5):887-890, 1990.Google Scholar[23] Andrzej Nedzusiak. Probability.

*Formalized Mathematics*, 1(4):745-749, 1990.Google Scholar[24] Andrzej Nedzusiak. σ-fields and probability.

*Formalized Mathematics*, 1(2):401-407, 1990.Google Scholar[25] Beata Perkowska. Functional sequence from a domain to a domain.

*Formalized Mathematics*, 3(1):17-21, 1992.Google Scholar[26] Yasunari Shidama and Noboru Endou. Lebesgue integral of simple valued function.

*Formalized Mathematics*, 13(1):67-71, 2005.Google Scholar[27] Andrzej Trybulec. Subsets of complex numbers.

*To appear in Formalized Mathematics.*Google Scholar[28] Andrzej Trybulec. Binary operations applied to functions.

*Formalized Mathematics*, 1(2):329-334, 1990.Google Scholar[29] Andrzej Trybulec. Tarski Grothendieck set theory.

*Formalized Mathematics*, 1(1):9-11, 1990.Google Scholar[30] Andrzej Trybulec. On the sets inhabited by numbers.

*Formalized Mathematics*, 11(4):341-347, 2003.Google Scholar[31] Michał J. Trybulec. Integers.

*Formalized Mathematics*, 1(3):501-505, 1990.Google Scholar[32] Zinaida Trybulec. Properties of subsets.

*Formalized Mathematics*, 1(1):67-71, 1990.Google Scholar[33] Edmund Woronowicz. Relations and their basic properties.

*Formalized Mathematics*, 1(1):73-83, 1990.Google Scholar[34] Edmund Woronowicz. Relations defined on sets.

*Formalized Mathematics*, 1(1):181-186, 1990.Google Scholar

**Published Online**: 2008-06-09

**Published in Print**: 2006-01-01

**Citation Information: **Formalized Mathematics, Volume 14, Issue 2, Pages 53–70, ISSN (Online) 1898-9934, ISSN (Print) 1426-2630, DOI: https://doi.org/10.2478/v10037-006-0008-x.

This content is open access.

Here you can find all Crossref-listed publications in which this article is cited. If you would like to receive automatic email messages as soon as this article is cited in other publications, simply activate the “Citation Alert” on the top of this page.

[1]

Noboru Endou

[2]

Yasushige Watase, Noboru Endou, and Yasunari Shidama

[3]

Hiroshi Yamazaki, Noboru Endou, Yasunari Shidama, and Hiroyuki Okazaki

[4]

Noboru Endou, Keiko Narita, and Yasunari Shidama

[5]

Noboru Endou, Yasunari Shidama, and Keiko Narita

[6]

Keiko Narita, Noboru Endou, and Yasunari Shidama

[7]

Hiroyuki Okazaki and Yasunari Shidama

[8]

Noboru Endou, Hiroyuki Okazaki, and Yasunari Shidama

[9]

Keiko Narita, Noboru Endou, and Yasunari Shidama

[10]

Keiko Narita, Noboru Endou, and Yasunari Shidama

[11]

Noboru Endou, Keiko Narita, and Yasunari Shidama

[12]

Keiko Narita, Noboru Endou, and Yasunari Shidama

[13]

Yasushige Watase, Noboru Endou, and Yasunari Shidama

## Comments (0)