Lebesgue's Theory of Integration: The Untouched Classic

by Rahul Jain

Overview

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.

Product Details

ISBN-13:	9789819611683
Publisher:	Springer Nature Singapore
Publication date:	05/11/2025
Pages:	321
Product dimensions:	6.61(w) x 9.45(h) x (d)

About the Author

Rahul Jain, Ph.D., is Deputy Inspector General at the Central Armed Police Force in New Delhi, India. His academic journey commenced at Kurukshetra University, where he completed his undergraduate studies. He later pursued postgraduate and doctoral studies at the Indian Institute of Science (IISc) and the Tata Institute of Fundamental Research Centre for Applied Mathematics (TIFR-CAM) from 2001 to 2006.

Dr. Jain’s research contributions have been recognized and published in esteemed journals, including in Computers and Mathematics with Applications. These publications underscore his proficiency in addressing complex mathematical problems with rigor and precision. Actively participating in academic events, he attended Trimester Schools in Italy and Portugal, presenting a paper in France on “Propagation and cancellation of singularities in a class of Fuchsian operators and their perturbations”.

Table of Contents

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.