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This book presents a unified treatise of the theory of measure and integration. In the setting of a general measure space, every concept is defined precisely and every theorem is presented with a clear and complete proof with all the relevant details. Counter-examples are provided to show that certain conditions in the hypothesis of a theorem cannot be simply dropped. The dependence of a theorem on earlier theorems is explicitly indicated in the proof, not only to facilitate reading but also to delineate the structure of the theory. The precision and clarity of presentation make the book an ideal textbook for a graduate course in real analysis while the wealth of topics treated also make the book a valuable reference work for mathematicians.
The book is also very helpful to graduate students in statistics and electrical engineering, two disciplines that apply measure theory.
Readership: Mathematicians and graduate students in analysis & differential equations.
- Sales Rank: #367891 in Books
- Published on: 2014-08-12
- Original language: English
- Number of items: 1
- Dimensions: 8.80" h x 1.70" w x 5.90" l, 2.73 pounds
- Binding: Paperback
- 840 pages
Review
Reviews of the Previous Editions:
"Finally, I recommend this book for a student who is helped by a good adviser." -- Mathematical Reviews
"Every concept is defined precisely and every theorem is presented with a detailed and complete proof." -- Mathematics Abstracts
"It is particularly suitable for a one-year course at the graduate level." -- Zentralblatt MATH
From the Inside Flap
This book presents a unified treatise of the theory of measure and integration. In the setting of a general measure space, every concept is defined precisely and every theorem is presented with a clear and complete proof with all the relevant details. Counter-examples are provided to show that certain conditions in the hypothesis of a theorem cannot be simply dropped. The dependence of a theorem on earlier theorems is explicitly indicated in the proof, not only to facilitate reading but also to delineate the structure of the theory. The precision and clarity of presentation make the book an ideal textbook for a graduate course in real analysis while the wealth of topics treated also make the book a valuable reference work for mathematicians.
The book is also very helpful to graduate students in statistics and electrical engineering, two disciplines that apply measure theory.
Most helpful customer reviews
10 of 10 people found the following review helpful.
A very digestible book on measure theory
By Mansour Kalantar
One of the difficulty of studying a math book is to figure out the details of a proof. In graduate texts there are frequent claims in the course of a proof that the authors make and the readers are supposed to check by themselves. If you do not have access to a professor this will cause problems. In Yeh’s book all the relevant details are presented and things are crystal clear. On the other hand the theorems are presented very precisely and the materials it covers is huge. Just take a look at the contents. The 3ed edition is the same as the second plus 50 pages of more material added at the end of the book and tens of more exercises. This is an excellent book for self-study at graduate level written in a reader friendly manner.
6 of 6 people found the following review helpful.
An excellent book for self-study.
By Daniel Kjær
Yeh's manual in the theory of measure and integration.
This work has intrigued me to an extent like nothing else in the field of mathematics, not only because of the content, but also because the method of presentation in an unusual degree made it suitable for self-study. This book contains all the theory and problems needed for a student to obtain a good background in real analysis assuming only calculus. The author is mindful of the troubles of beginners; each theorem is provided with a detailed proof; each chapter systematically starts where the previous left off; he includes an abundant supply of exercises; et cetera.
I would definitely recommend that you use this book as your primary guide in real analysis.
6 of 7 people found the following review helpful.
This book easily passes off as an encyclopedia in real analysis
By Nehemiah Leong
This book easily passes off as an encyclopedia in real analysis. I applause prof Yeh for his clarity in writing and the attention he paid to small details in all of his proofs. These small details are often those things that make the proof to a theorem laden with gaps which makes it hard to follow. The style of writing is lucid so that anyone with a sound grounding in introductory analysis would find the book an easy read. Although I have yet to plough through the entire book (> 700 pages), I was captivated by the first few pages on his exposition on the sigma algebra and limit superior and inferior of sets. Prof Yeh has the unique ability to explain concepts and turn confusion into understanding. I photocopied his second edition and when his third edition was released, guess what? I bought it!
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