A radical approach to Lebesgue’s theory of integration. (English) Zbl 1165.00001

Bressoud, David M.

MAA Textbooks. Cambridge: Cambridge University Press; Washington, DC: Mathematical Association of America (MAA) (ISBN 978-0-521-71183-8/pbk; 978-0-521-88474-7/hbk). xiv, 329 p. (2008).

This book is an introduction to measure theory and Lebesgue integration and it is dedicated to advanced undergraduate and graduate students in mathematics.
Informed by history, attempting to the motivations, uncertainties, and difficulties surrounding the key concepts of the field, this book is devoted to explain the answers to the five historical questions that changed the nature of analysis forever and that led to the development of measure theory and Lebesgue integration.
Moreover, this is a story of any contributions by many members of a large community of mathematicians working on different pieces of the puzzle in the late nineteenth, early twentieth century.

Reviewer: Octavian Lipovan (Timişoara)

MSC:

00-01	Introductory exposition (textbooks, tutorial papers, etc.) pertaining to mathematics in general
26-01	Introductory exposition (textbooks, tutorial papers, etc.) pertaining to real functions
28-01	Introductory exposition (textbooks, tutorial papers, etc.) pertaining to measure and integration
28-03	History of measure and integration
26A42	Integrals of Riemann, Stieltjes and Lebesgue type
28A12	Contents, measures, outer measures, capacities
28A25	Integration with respect to measures and other set functions