The Integral: A Crux for Analysis

Steven G. Krantz

iyn 2022 · Springer Nature

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This book treats all of the most commonly used theories of the integral. After motivating the idea of integral, we devote a full chapter to the Riemann integral and the next to the Lebesgue integral. Another chapter compares and contrasts the two theories. The concluding chapter offers brief introductions to the Henstock integral, the Daniell integral, the Stieltjes integral, and other commonly used integrals. The purpose of this book is to provide a quick but accurate (and detailed) introduction to all aspects of modern integration theory. It should be accessible to any student who has had calculus and some exposure to upper division mathematics. Table of Contents: Introduction / The Riemann Integral / The Lebesgue Integral / Comparison of the Riemann and Lebesgue Integrals / Other Theories of the Integral

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Steven G. Krantz was born in San Francisco, California in 1951. He received the B.A. degree from the University of California at Santa Cruz in 1971 and the Ph.D. from Princeton University in 1974. Krantz has taught at UCLA, Princeton University, Penn State, and Washington University in St. Louis. He has served as Chair of the latter department. Krantz has directed 9 Masters theses and 18 Ph.D. theses. He has been awarded the UCLA Alumni Foundation Distinguished Teaching Award, the Chauvenet Prize, and the Beckenbach Book Prize. Krantz has published over 155 scholarly articles and over 55 books. He is currently the Editor of the Notices of the American Mathematical Society.