A Modern Theory of Integration (Graduate Studies in Mathematics) The first version of integration that students see is the Riemann integral. Later, graduate students learn that the Lebesgue integral is "better" because it removes some restrictions on the integrands and the domains over which we integrate. Although this integral includes that of Lebesgue, its def
| Title | : | A Modern Theory of Integration (Graduate Studies in Mathematics) |
| Author | : | |
| Rating | : | 4.92 (486 Votes) |
| Asin | : | 0821808451 |
| Format Type | : | Hardcover |
| Number of Pages | : | 458 Pages |
| Publish Date | : | 2001-04-01 |
| Genre | : |
A comprehensive, beautifully written exposition of the Henstock-Kurzweil (gauge, Riemann complete) integral The theory of integration is one of the twin pillars on which analysis is built. The first version of integration that students see is the Riemann integral. Later, graduate students learn that the Lebesgue integral is "better" because it removes some restrictions on the integrands and the domains over which we integrate. However, there are still drawbacks to Lebesgue integration, for instance, dealing with the Fundamental Theorem of Calculus, or with "improper" integrals. This book is an introduction to a relatively new theory of the integral (called the "generalized Riemann integral" or the "Henstock-Kurzweil integral") that corrects the defects in the classical Riemann theory and both simplifies and extends the Lebesgue theory of integration. Although this integral includes that of Lebesgue, its definition is very close to the Riemann integral that is familiar to students from
Editorial : "The book presents its subject in a pleasing, didactically surprising, and well worth reading exposition. The proofs are, as a rule, easily understandable and the significance of the theorems that are worked through is illustrated by means of numerous examples. It can be recommended as a self-study book to every student with a basic foundation in analysis. It is also very suitable as a supplementary text for a course on integration on $\mathbf{R$." ---- Translated fromJahresbericht der Deutschen Mathematiker-Vereinigung
"A comprehensive, beautifully written exposition of the Henstock-Kurzweil (gauge, Riemann complete) integral There is an abundant supply of exercises which serve to make this book an excellent choice for a text for a course which would contain an elementary introduction to modern integration theory." ---- Zentralblatt MATH
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