Designed for the full-time analyst, physicist, engineer, or economist, this book attempts to provide its readers with most of the measure theory they will ever need. The author has consistently developed the concrete rather than the abstract aspects of topics treated. The major new feature of this third edition is the inclusion of a new chapter in which the author introduces the Fourier transform. Solutions to all problems are provided. As a self-contained text, this book is excellent for both self-study and the classroom.
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Editorial Reviews
From Scientific American
"This book, unusual in many respects, fully achieves its goal, a one-semester, concise but logically complete treatment of abstract integration. There are only 148 pages, making the book psychologically attractive and a price of $18..."
--This text refers to the
Paperback
edition.
Review
"This is a very attractive textbook… Unusual in many respects, [it] fully achieves its goal, a one-semester, concise but logically complete treatment of abstract integration. It is remarkable that [the author] has accomplished so much in so short a compass."
- Mathematical Reviews (review of the first edition)
"A number of valuable applications and a good collection of problems... A very interesting, well-informed book which draws on recent approaches not found in several commonly used texts."
- Zentralblatt Math (review of the second edition)
"The author succeeded in choosing the right level of generality and showed how a good combination of a measure and integration course and advanced calculus can be done. Strongly recommended to students as well as to teachers."
- EMS Newsletter (review of the second edition)
"...the author is a distinguished probabilist/analyst who has made seminal contributions to the interface of probability theory with PDEs/harmonic analysis/functional analysis; the flavor of all these subjects is brought out in the book, especially in chapters V-VII...[the] book can be highly rewarding, serving as a launching pad for an intensive study of any branch of analysis including probability theory."
--Current Science (review of the third edition)
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Most Helpful Customer Reviews
11 of 13 people found the following review helpful:
5.0 out of 5 stars
A perfect place to start Real Analysis,
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This review is from: Concise Introduction To The Theory Of Integration, A (Series in Pure Mathematics) (Paperback)
This is a perfect textbook for a one-semester course in measure and integration at a graduate level. It's concise but complete and detailed, rigour but motivated and inspiring. It's more technical than Bartle's little book on integration. It also has solution manual in the end to check on. I hope more readers enjoy such a wonderful germ written by a star form MIT.
5 of 12 people found the following review helpful:
3.0 out of 5 stars
Hard to understand!,
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This review is from: A Concise Introduction to the Theory of Integration (Hardcover)
I bought this book for my class, but honestly I felt hard to understand the concepts presented in this book.
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Inside This Book
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First Sentence:
We begin by recalling a few basic facts about the integration theory which is usually introduced in advanced calculus. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
exact covers, countable cover, monotone class, measurable map, finite measure space, coordinate chart, orthonormal sequence, measurable functions, smooth region Key Phrases - Capitalized Phrases (CAPs): (learn more)
Fatou's Lemma, Fubini's Theorem, Lebesgue's Dominated Convergence Theorem, Monotone Convergence Theorem, Green's Identity, Mean Value Property, Tonelli's Theorem, Lebesgue's Differentiation Theorem, Taylor's Theorem, Dini's Lemma, Fundamental Theorem of Calculus New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
We begin by recalling a few basic facts about the integration theory which is usually introduced in advanced calculus. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
exact covers, countable cover, monotone class, measurable map, finite measure space, coordinate chart, orthonormal sequence, measurable functions, smooth region Key Phrases - Capitalized Phrases (CAPs): (learn more)
Fatou's Lemma, Fubini's Theorem, Lebesgue's Dominated Convergence Theorem, Monotone Convergence Theorem, Green's Identity, Mean Value Property, Tonelli's Theorem, Lebesgue's Differentiation Theorem, Taylor's Theorem, Dini's Lemma, Fundamental Theorem of Calculus New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 6
books:
See all 6 books this book cites
20
books
cite this book:
See all 20 books citing this book
- Measure Theory and Fine Properties of Functions (Studies in Advanced Mathematics) by Lawrence C. Evans on page 182
- The Principles of Mathematical Analysis (International Series in Pure & Applied Mathematics) by Walter Rudin on page 91
- Measure and Integral: An Introduction to Real Analysis (Chapman & Hall/CRC Pure and Applied Mathematics) by Richard Wheeden in Front Matter
- Theory of Ordinary Differential Equations by Earl A. Coddington on page 94
- Theory of Ordinary Differential Equations by Earl A. Coddington on page 94
See all 6 books this book cites
- Measures, Integrals and Martingales by René L. Schilling in Back Matter (1), and Back Matter (2)
- Boundary Value Problems for Analytic Functions (Series in Pure Mathematics) by Jian-Ke Lu in Front Matter
- An Introduction to Markov Processes (Graduate Texts in Mathematics) by Daniel W. Stroock in Back Matter
- Complex Variable Methods in Plane Elasticity (Series in Pure Mathematics) by Jian-Ke Lu in Front Matter
- Backgrounds of Arithmetic and Geometry: An Introduction (Pure Mathematics Series , Vol 23) by Radu Miron in Front Matter
See all 20 books citing this book
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