J. J. Duistermaat, J. A. C. Kolk, "Multidimensional Real Analysis", volumes I and II
Cambridge University Press | 2004
Volume I - Differentiation | ISBN 0521551145 | Pages 440 | PDF | 28.1 MB
Volume II - Integration | ISBN 0521829259 | Pages 394 | PDF | 24.6 MB

国内的教材注重单唯分析，多维分析是一个缺陷。如同我们学数理统计，大部分老师主要讲随机变量及在此基础上的分布和推断。但是一旦翻开计量经济学书籍，发现都是以随机向量作为最基本的工具进行论述。实分析，同样要走向多维。这本多维实分析非常有名，内容安排上做到自封闭，可以用于课堂教学或者自己学习。世界图文影印此书后，清华图书馆即向本科生推荐作为教学参考书或者课堂主要教材之一。

在pinggu上找了一下，发现没有这本书。在此提供vol.1的下载链接。vol.2的链接已经失效。感兴趣的网友可以购买纸质版，或者在网上找一下电子版。
vol.1下载
http://www.yuyucollege.cn/read-htm-tid-145955-fpage-8.html

http://hotfile.com/dl/877741/88c880f/0521551145.rar.html    【我刚下载，该链接有效】
http://rapidshare.com/files/227437384/0521551145.rar          【这个没试过】

vol.2的下载：热心网友在网上找一下吧。我找到的链接已经失效。

Editorial Reviews
Volume I
Part one of the authors' comprehensive and innovative work on multidimensional real analysis. This book is based on extensive teaching experience at Utrecht University and gives a thorough account of differential analysis in multidimensional Euclidean space. It is an ideal preparation for students who wish to go on to more advanced study. The notation is carefully organized and all proofs are clean, complete and rigorous. The authors have taken care to pay proper attention to all aspects of the theory. In many respects this book presents an original treatment of the subject and it contains many results and exercises that cannot be found elsewhere. The numerous exercises illustrate a variety of applications in mathematics and physics. This combined with the exhaustive and transparent treatment of subject matter make the book ideal as either the text for a course, a source of problems for a seminar or for self study.
"Throughout the notation is carefully organized and all proofs are complete and rigorous. The text is completed by carefully worked examples, many of them are illustrated by drawings. A special feature of the book is the extensive collection of exercises �� The book is a good preparation for readers who wish to go on to more advanced studies in analysis. It can be also highly recommended as a text for a course or for self study."-Zentralblatt fur Mathematik
Volume II
Part two of the authors' comprehensive and innovative work on multidimensional real analysis. This book is based on extensive teaching experience at Utrecht University and gives a thorough account of integral analysis in multidimensional Euclidean space. It is an ideal preparation for students who wish to go on to more advanced study. The notation is carefully organized and all proofs are clean, complete and rigorous. The authors have taken care to pay proper attention to all aspects of the theory. In many respects this book presents an original treatment of the subject and it contains many results and exercises that cannot be found elsewhere. The numerous exercises illustrate a variety of applications in mathematics and physics. This combined with the exhaustive and transparent treatment of subject matter make the book ideal as either the text for a course, a source of problems for a seminar or for self study.
''Throughout the text is carefully organized, proofs are complete and rigorous and the material is completed by carefully worked examples.'- Zentralblatt fur Mathematik

Numerous and innovative exercises with partial solutions to aid the reader
Includes new results and perspectives on the subject
Fully class tested and based on extensive teaching experience