myArmoury.com: Measure Theory

Measure Theory

by Donald L. Cohn

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Average customer rating:

(7 votes)

Edition: Paperback

Other editions available: Hardcover, Digital

27 third-party copies available from: $43.19

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Product Description:

Intended as a straightforward introduction to measure theory, this textbook emphasizes those topics relevant and necessary to the study of analysis and probability theory. The first five chapters deal with abstract measure and integration. At the end of these chapters, the reader will appreciate the elements of integration. Chapter 6, on differentiation, includes a treatment of changes of variables in Rd. A unique feature of the book is the introductory, yet comprehensive treatment of integration on locally Hausdorff spaces, of the analytic and Borel subsets of Polish spaces, and of Haar measures on locally compact groups. Measure Theory provides the reader with tools needed for study in several areas of current interest, in particular harmonic analysis and probability theory, and is a valuable reference tool.

Accessories:
• Undergraduate Analysis (Undergraduate Texts in Mathematics)
• Advanced Calculus: A Differential Forms Approach

Customer Reviews:

A good introduction to Measure Theory
Review date: 2009-12-17

I used this book for my graduate measure theory class. We covered the first seven chapters. The book is written in a clear fashion and is easy to follow. It is concise and at the same time is almost self contained.

The first chapter gives an introduction to measure theory. It deals with sigma algebras, measures, outer measures, completeness and regularity. The lebesgue measure is also introduced in this chapter.

The second chapter starts of measurable functions. It then proceeds to almost sure properties followed by integration. These are followed by the theorem: Monotone convergence theorem, Beppo Levi theorem, Fatou's Lemma and Dominated Convergence Theorem. The chapter also discusses briefly on Riemann integrals.

The third chapter is on different modes of convergence. It proves the Egoroff theorem. This is followed by the definition and properties of Banach spaces.

The fourth chapter discusses signed measures. The Hahn decomposition theorem and Jordan decomposition theorems are proved. It is followed by absolutely continuous measures which leads to Radon-Nikodym theorem.

The fifth chapter deals with Product measures. The most important theorem in this chapter is the Fubini's theorem which is proved in the second section.

The sixth chapter is on differentiation of measures. Proves Fundamental theorem of calculus.

The seventh chapter is on Hausdorff spaces and Riesz representation theorem followed by properties of regular measures (Lusin's theorem)

Chapter 8 is on Polish Spaces and Analytic Sets

Chapter 9 is on Haar Measures

(We did not cover the last two chapters in this course)

A great companion to Folland or Rudin
Review date: 2009-05-03

I believe that Cohn's Measure Theory is a fantastic companion for learning Analysis in concert with one of the denser books from Folland or Rudin. While still covering a wide range of subjects, Cohn's exposition is much more conducive to the learning experience than either of the other two, in my opinion. He does an excellent job of explaining his reasoning in proofs, while still leaving enough to the reader to get them involved in the process.

The exercises are also very well done, and range over a wide difficulty level, though are easier, on the whole, than those in the other two books.

This book, even by itself, will give you a VERY strong foundation in measure theory and integration theory, and has the benefit of being very affordable.

A Book of Clarity and Rigor
Review date: 2008-02-07

Cohn's Measure Theory is one of the most clear, rigorous and easy-going textbooks I have ever read. All theorems, propositions, lemmas are stated in full; there is neither a missing hypothesis, nor an obscure conclusion. Moreover, the number of errors in the book is minimal when compared to other texts in mathematics.

I like
Review date: 2006-11-08

Very technical yet readable book. Cohn does a great job in the explanation of integrability. The appendix is very complete and gives you a first hand help on the topics discussed trough out the book. I used the book for Real Analysis and it has been of great help.

The book is very good, but Amazon's digital upgrade is very poor
Review date: 2006-06-24

I bought the book, and also the Amazon upgrade to digital version, so I could read the book online. It was a great disappointment. The viewing screen is so small that it cannot show a full page; I tried to print out a few pages, but the printing software froze my printer; and then the program cut me off, claiming I had exceeded the limits, which I had not been told about. I tried to get a refund a few hours after I had bought it, but customer service was unhelpful. They didn't even know what an Amazon Book Upgrade was, and then they claimed, mistakenly, that upgrades cannot be returned. Finally, they told me I had viewed more than the allowance, which was not true. Overall, an awful experience. It's just $10 wasted, but my advice is: DON'T GET THE UPGRADE.

Product Details/Specifications:

Authors:
Donald L. Cohn

Recording label: Birkhäuser Boston
Publishers:
Birkhäuser Boston

Manufacturer: Birkhäuser Boston
EAN: 9780817630034
Binding: Paperback
Dewey decimal number: 511
ISBN: 0817630031
Number of items: 1
Number of pages: 388
Publication date: 1994-01-01