國立虎尾科技大學 |

Lebesgue's theory of integration = the untouched classic /

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Lebesgue's theory of integration/ by Rahul Jain.
Reminder of title:	the untouched classic /
Author:	Jain, Rahul.
Published:	Singapore :Springer Nature Singapore : : 2025.,
Description:	xix, 321 p. :ill., digital ; : 24 cm.;
Contained By:	Springer Nature eBook
Subject:	Lebesgue integral. -
Online resource:	https://doi.org/10.1007/978-981-96-1169-0
ISBN:	9789819611690

Lebesgue's theory of integration = the untouched classic /
Jain, Rahul.

Lebesgue's theory of integrationthe untouched classic /[electronic resource] :by Rahul Jain. - Singapore :Springer Nature Singapore :2025. - xix, 321 p. :ill., digital ;24 cm.

The Integration before Riemann -- The Definition of Integral Given by Riemann -- Geometric Definition of the Integral -- The Functions of the Bounded Variation -- The Search for Primitive Functions -- The Integration Defined with the Help of Primitive Functions -- The Definite Integral of Summable Functions -- The Indefinite Integral of Summable Functions -- The Seach of Primitive Functions. The Existence of Derivatives -- The Totalisation -- The Integral of Steiltjes.

This is an invaluable book that presents the original work published in French, in 1904, by Henry Leon Lebesgue, the creator of the theory of integration. Translated into English for the first time, the book offers readers a unique opportunity to explore Lebesgue's groundbreaking ideas and delves into the mind of one of the greatest mathematicians in history. The book provides historical context and explanations that enhance readers' comprehension and appreciation of the material. Covering a wide range of topics, from the integration before Riemann to the search for primitive functions, it offers a comprehensive understanding of Lebesgue's theories and their significance in the field of mathematics. It inspires readers to explore further in the field, stimulates new ideas, and opens avenues for future research. The book bridges the gap between theory and practice by providing examples and applications that contributed to the development of Lebesgue integration theory. The book serves as a valuable resource for courses in analysis, measure theory, and Lebesgue integration theory, providing students with the opportunity to study the original work of Lebesgue and deepen their understanding of integration theory. It is meant for a broad audience, including advanced undergraduate and graduate students, mathematics scholars, researchers, educators, and enthusiasts, seeking a comprehensive understanding of Lebesgue's theories and the historical development of integration theory. Mathematicians and researchers will find this book essential for its historical significance and the preservation of important mathematical literature.

ISBN: 9789819611690

Standard No.: 10.1007/978-981-96-1169-0doiSubjects--Topical Terms:

786722
Lebesgue integral.

LC Class. No.: QA312

Dewey Class. No.: 515.42

Lebesgue's theory of integration = the untouched classic /
LDR:03195nam a2200337 a 4500 001 1162521
003 DE-He213
005 20250511130332.0
006 m d
007 cr nn 008maaau
008 251029s2025 si s 0 eng d
020 $a 9789819611690 $q (electronic bk.)
020 $a 9789819611683 $q (paper)
024 7 $a 10.1007/978-981-96-1169-0 $2 doi
035 $a 978-981-96-1169-0
040 $a GP $c GP
041 1 $a eng $h fre
050 4 $a QA312
072 7 $a PBKL $2 bicssc
072 7 $a MAT034000 $2 bisacsh
072 7 $a PBKL $2 thema
082 0 4 $a 515.42 $2 23
090 $a QA312 $b .J25 2025
100 1 $a Jain, Rahul. $3 885376
240 1 0 $a Leçons sur l'intégration et la recherche des fonctions primitives. $l English
245 1 0 $a Lebesgue's theory of integration $h [electronic resource] : $b the untouched classic / $c by Rahul Jain.
260 $a Singapore : $c 2025. $b Springer Nature Singapore : $b Imprint: Springer,
300 $a xix, 321 p. : $b ill., digital ; $c 24 cm.
505 0 $a The Integration before Riemann -- The Definition of Integral Given by Riemann -- Geometric Definition of the Integral -- The Functions of the Bounded Variation -- The Search for Primitive Functions -- The Integration Defined with the Help of Primitive Functions -- The Definite Integral of Summable Functions -- The Indefinite Integral of Summable Functions -- The Seach of Primitive Functions. The Existence of Derivatives -- The Totalisation -- The Integral of Steiltjes.
520 $a This is an invaluable book that presents the original work published in French, in 1904, by Henry Leon Lebesgue, the creator of the theory of integration. Translated into English for the first time, the book offers readers a unique opportunity to explore Lebesgue's groundbreaking ideas and delves into the mind of one of the greatest mathematicians in history. The book provides historical context and explanations that enhance readers' comprehension and appreciation of the material. Covering a wide range of topics, from the integration before Riemann to the search for primitive functions, it offers a comprehensive understanding of Lebesgue's theories and their significance in the field of mathematics. It inspires readers to explore further in the field, stimulates new ideas, and opens avenues for future research. The book bridges the gap between theory and practice by providing examples and applications that contributed to the development of Lebesgue integration theory. The book serves as a valuable resource for courses in analysis, measure theory, and Lebesgue integration theory, providing students with the opportunity to study the original work of Lebesgue and deepen their understanding of integration theory. It is meant for a broad audience, including advanced undergraduate and graduate students, mathematics scholars, researchers, educators, and enthusiasts, seeking a comprehensive understanding of Lebesgue's theories and the historical development of integration theory. Mathematicians and researchers will find this book essential for its historical significance and the preservation of important mathematical literature.
650 0 $a Lebesgue integral. $3 786722
650 0 $a Numerical integration. $3 527668
650 1 4 $a Measure and Integration. $3 672015
650 2 4 $a Special Functions. $3 672152
650 2 4 $a Number Theory. $3 672023
710 2 $a SpringerLink (Online service) $3 593884
773 0 $t Springer Nature eBook
856 4 0 $u https://doi.org/10.1007/978-981-96-1169-0
950 $a Mathematics and Statistics (SpringerNature-11649)