| Hardcover ISBN: | 978-0-88385-343-6 |
| Product Code: | DOL/37 |
| List Price: | $65.00 |
| MAA Member Price: | $48.75 |
| AMS Member Price: | $48.75 |
| eBook ISBN: | 978-0-88385-915-5 |
| Product Code: | DOL/37.E |
| List Price: | $60.00 |
| MAA Member Price: | $45.00 |
| AMS Member Price: | $45.00 |
| Hardcover ISBN: | 978-0-88385-343-6 |
| eBook: ISBN: | 978-0-88385-915-5 |
| Product Code: | DOL/37.B |
| List Price: | $125.00 $95.00 |
| MAA Member Price: | $93.75 $71.25 |
| AMS Member Price: | $93.75 $71.25 |
| Hardcover ISBN: | 978-0-88385-343-6 |
| Product Code: | DOL/37 |
| List Price: | $65.00 |
| MAA Member Price: | $48.75 |
| AMS Member Price: | $48.75 |
| eBook ISBN: | 978-0-88385-915-5 |
| Product Code: | DOL/37.E |
| List Price: | $60.00 |
| MAA Member Price: | $45.00 |
| AMS Member Price: | $45.00 |
| Hardcover ISBN: | 978-0-88385-343-6 |
| eBook ISBN: | 978-0-88385-915-5 |
| Product Code: | DOL/37.B |
| List Price: | $125.00 $95.00 |
| MAA Member Price: | $93.75 $71.25 |
| AMS Member Price: | $93.75 $71.25 |
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Book DetailsDolciani Mathematical ExpositionsVolume: 37; 2009; 107 pp
This book is an outline of the core material in the standard graduate-level real analysis course. It is intended as a resource for students in such a course as well as others who wish to learn or review the subject. On the abstract level, it covers the theory of measure and integration and the basics of point set topology, functional analysis, and the most important types of function spaces. On the more concrete level, it also deals with the applications of these general theories to analysis on Euclidean space: the Lebesgue integral, Hausdorff measure, convolutions, Fourier series and transforms, and distributions. The relevant definitions and major theorems are stated in detail. Proofs, however, are generally presented only as sketches, in such a way that the key ideas are explained but the technical details are omitted. In this way a large amount of material is presented in a concise and readable form.
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Table of Contents
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Chapters
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Prologue: Notation, Terminology, and Set Theory
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Chapter 1. Topology
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Chapter 2. Measure and Integration: General Theory
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Chapter 2. Measure and Integration: Constructions and Special Examples
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Chapter 4. Rudiments of Functional Analysis
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Chapter 5. Function Spaces
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Chapter 6. Topics in Analysis on Euclidean Space
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Additional Material
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Reviews
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This work serves as a Baedeker to the more accessible parts of the terrain of advanced real analysis, providing an overview for those less familiar, a refresher for those more so, and a key to the features of that terrain, including what high points and cultural monuments to visit if planning to explore the subject more seriously. Intended as a guide for grduate students preparing for qualifying exams.
F. E. J. Linton, Choice -
The book covers material that is standardly taught at universities in graduate courses of real analysis and measure theory, plus some extra material from point-set topology and functional analysis, including some basic facts from the theory of function spaces. On the one hand it is written in a very skillful manner in a brief and concise reader-friendly way, but, on the other hand, the text is surprisingly comprehensive. ... The book is a wonderful example of how much can be achieved in a relatively small space.
Lubos Pick, Mathematical Reviews
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RequestsReview Copy – for publishers of book reviewsAccessibility – to request an alternate format of an AMS title
- Book Details
- Table of Contents
- Additional Material
- Reviews
- Requests
This book is an outline of the core material in the standard graduate-level real analysis course. It is intended as a resource for students in such a course as well as others who wish to learn or review the subject. On the abstract level, it covers the theory of measure and integration and the basics of point set topology, functional analysis, and the most important types of function spaces. On the more concrete level, it also deals with the applications of these general theories to analysis on Euclidean space: the Lebesgue integral, Hausdorff measure, convolutions, Fourier series and transforms, and distributions. The relevant definitions and major theorems are stated in detail. Proofs, however, are generally presented only as sketches, in such a way that the key ideas are explained but the technical details are omitted. In this way a large amount of material is presented in a concise and readable form.
-
Chapters
-
Prologue: Notation, Terminology, and Set Theory
-
Chapter 1. Topology
-
Chapter 2. Measure and Integration: General Theory
-
Chapter 2. Measure and Integration: Constructions and Special Examples
-
Chapter 4. Rudiments of Functional Analysis
-
Chapter 5. Function Spaces
-
Chapter 6. Topics in Analysis on Euclidean Space
-
This work serves as a Baedeker to the more accessible parts of the terrain of advanced real analysis, providing an overview for those less familiar, a refresher for those more so, and a key to the features of that terrain, including what high points and cultural monuments to visit if planning to explore the subject more seriously. Intended as a guide for grduate students preparing for qualifying exams.
F. E. J. Linton, Choice -
The book covers material that is standardly taught at universities in graduate courses of real analysis and measure theory, plus some extra material from point-set topology and functional analysis, including some basic facts from the theory of function spaces. On the one hand it is written in a very skillful manner in a brief and concise reader-friendly way, but, on the other hand, the text is surprisingly comprehensive. ... The book is a wonderful example of how much can be achieved in a relatively small space.
Lubos Pick, Mathematical Reviews
