Real and Functional Analysis (Graduate Texts in Mathematics) | 
 enlarge | Author: Serge Lang
Publisher: Springer
Category: Book
List Price: $69.95
Buy New: $50.48
You Save: $19.47 (28%)
New (24) Used (13) from $42.00
Rating:  3 reviews
Sales Rank: 152689
Media: Hardcover
Edition: 3rd
Pages: 600
Number Of Items: 1
Shipping Weight (lbs): 2.2
Dimensions (in): 9.3 x 6.3 x 1.5
ISBN: 0387940014
Dewey Decimal Number: 515
EAN: 9780387940014
Publication Date: April 29, 1993
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Shipping: International shipping available
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Product Description
This book is meant as a text for a first-year graduate course in analysis. In a sense, the subject matter covers the same topics as elementary calculus - linear algebra, differentiation, integration - but treated in a manner suitable for people who will be using it in further mathematical investigations. The book begins with point-set topology, essential for all analysis. The second part deals with the two basic spaces of analysis, Banach and Hilbert spaces. The book then turns to the subject of integration and measure. After a general introduction, it covers duality and representation theorems, some applications (such as Dirac sequences and Fourier transforms), integration and measures on locally compact spaces, the Riemann-Stjeltes integral, distributions, and integration on locally compact groups. Part four deals with differential calculus (with values in a Banach space). The next part deals with functional analysis. It includes several major spectral theorems of analysis, showing how one can extend to infinite dimensions certain results from finite-dimensional linear algebra; a discussion of compact and Fredholm operators; and spectral theorems for Hermitian operators. The final part, on global analysis, provides an introduction to differentiable manifolds. The text includes worked examples and numerous exercises, which should be viewed as an integral part of the book. The organization of the book avoids long chains of logical interdependence, so that chapters are as independent as possible. This allows a course using the book to omit material from some chapters without compromising the exposition of material from later chapters.
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| Customer Reviews:
 Much better than Royden! June 8, 2005
Reviewer
8 out of 8 found this review helpful
It drove me up the wall, in my first course on measure and integration, that integration was first done for positive functions, then for real functions by writing them as a difference of positive functions, then complex functions in terms of real and imaginary parts. Why couldn't you just integrate real-valued functions
intrinsically, without the silly decomposition into positive and negative parts?
After that course, I found Lang's book. What a blessing to see that you can just integrate in infinite-dimensional spaces right from the start. I can't understand why virtually all books on integration theory still succumb to the "positive functions first" approach.
One of a kind ! June 26, 2007
Louis De Thanhoffer Voelcsey
5 out of 5 found this review helpful
Up to my knowledge, this is the only book that constructs the Lebesgue integral for functions to a general Banach-space instead of the real numbers (thus saving us from the unnecessary and esthetically dissapointing construction through positive and negative functions).
I don't know how Lang does it, but eerytime you'll pick up one of his books, you'll marvel at the beauty of mathematics !
 Overall, A Good Book January 14, 2005
Applied Math Student (USA)
4 out of 4 found this review helpful
I've read several analysis books and this is one of the better ones that I have read. It covers a variety of interesting and useful topics and the exposition is clear. It's presentation is a bit more abstract than some others starting with some functional-analytic concepts before doing integration in that framework. However, if you want to study stochastic analysis, getting in this frame of mind will definitely help your understanding of stochastic integration. For a truly thorough understaning of the subject, I recommend purchasing this book as well as the somewhat easier "Lebesgue Integration on Euclidean Space" by Frank Jones - the two together cost about the same as Royden, Rudin, or the terrible book by Aliprantis.
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