Modern View of the Riemann Integral

Alberto Torchinsky is Emeritus Professor of Mathematics at Indiana University Bloomington. His research interests are centered on harmonic and real analysis. He has authored several other books, including the widely cited LNM 1381, Weighted Hardy Spaces, with Jan-Olov Strömberg. Prior to Indiana University, he held positions at the University of Illinois and Cornell University, having received his PhD at the University of Chicago under A. P. Calderón.

“There are 108 references. Most of them make use of the Riemann integral and a lot of them arerelated to deep questions. … based on the results in this book, that new results will be obtained in the future and that this book will represent the state of the art in 2022.” (Richard Becker, Mathematical Reviews, September, 2023)“The book presents a detailed and well-written treatise on the Riemann integral and its many variants and properties. … The book is not quite a text book, but an independent source book for results. It is very useful say for graduate students preparing for qualifying exams … . It is also useful for a researcher interested if their research involves variants of the Riemann integral. The proofs could be used in instruction, and are often quite nice.” (Sylvester Eriksson-Bique, zbMATH 1509.26003, 2023)

• Preface.- Chapter 1. Introduction.- Chapter 2. The ����–Riemann Integral.- Chapter 3. A Convergence Theorem.- Chapter 4. The Modified ����–Riemann Sums.- Chapter 5. The Pattern and Uniform Integrals.- Chapter 6. The Improper and Dominated Integrals.- Chapter 7. Coda.- Appendix I.- Appendix II.- References.- Index.