Series in Real Analysis - Vol. 9
THEORIES OF INTEGRATION
The Integrals of Riemann, Lebesgue, Henstock-Kurzweil, and McShane
by Douglas S Kurtz & Charles W Swartz (New Mexico State University, USA)
This book presents a historical development of the integration theories of Riemann, Lebesgue, Henstock–Kurzweil, and McShane, showing how new theories of integration were developed to solve problems that earlier theories could not handle. It develops the basic properties of each integral in detail and provides comparisons of the different integrals. The chapters covering each integral are essentially independent and can be used separately in teaching a portion of an introductory course on real analysis. There is a sufficient supply of exercises to make the book useful as a textbook.
Contents:
- Riemann Integral
- Convergence Theorems and the Lebesgue Integral
-
Fundamental Theorem of Calculus and the Henstock–Kurzweil Integral
- Absolute Integrability and the McShane Integral
Readership: Upper-level undergraduate students, beginning graduate students,
lecturers and researchers interested in integration theory.
“The authors are to be commended for covering a lot of ground in less than 300 pages ... Two possible courses that could be developed using this book are: First, if students have had an analysis course on proofs, limits, continuity and differentiation, this text could be used for a following course on Riemann and Lebesgue integration. Secondly, it could be used for a course that wishes to survey integration theories. It would also make for suitable independent reading. Priced at $56, it is good value.”
“This book can be recommended as a textbook for upper-level undergraduate students and beginning graduate students. Being clearly written and self-contained it can be also used for self study.”
| Studia Universitatis “Babeş-Bolyai”, Series Mathematica |
| 284pp |
Pub. date: Jun 2004 |
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