数学本科专业经典教材7 — 实分析 Real analysis (Folland)


作者: Gerald B. Folland
出版社: Wiley
副标题: Modern Techniques and Their Applications
出版年: 1999-4-7
页数: 408
定价: USD 179.00
装帧: Hardcover
丛书: Pure and Applied Mathematics: A Wiley Series of Texts, Monographs, and Tracts
ISBN: 9780471317166


An in-depth look at real analysis and its applications-now expanded and revised.
This new edition of the widely used analysis book continues to cover real analysis in greater detail and at a more advanced level than most books on the subject. Encompassing several subjects that underlie much of modern analysis, the book focuses on measure and integration theory, point set topology, and the basics of functional analysis. It illustrates the use of the general theories and introduces readers to other branches of analysis such as Fourier analysis, distribution theory, and probability theory.
This edition is bolstered in content as well as in scope-extending its usefulness to students outside of pure analysis as well as those interested in dynamical systems. The numerous exercises, extensive bibliography, and review chapter on sets and metric spaces make Real Analysis: Modern Techniques and Their Applications, Second Edition invaluable for students in graduate-level analysis courses. New features include:
* Revised material on the n-dimensional Lebesgue integral.
* An improved proof of Tychonoff's theorem.
* Expanded material on Fourier analysis.
* A newly written chapter devoted to distributions and differential equations.
* Updated material on Hausdorff dimension and fractal dimension.








应该说Folland的实分析是大三一年最认真读过的一本书了。这本书一共11章，读过的大概是1-3 6-9 11。
大三上学期的时候我选修了一门本硕贯通课程“高等实分析”，我们的教材用的是Stein的实分析Ch6和泛函分析Ch1-3, 8. 老师第一节课就给我们推荐了Folland这本参考书。
初读此书的时候是感觉不适的，因为的确有不少证明过程没有给出details. 然而到后面却发现，书中的逻辑链条异常清晰，感觉每一节都是上一节逻辑的必然。
习题很赞，有一些非常经典的例子，认真做了的大概是Ch1-3 6 8 9.
L^p空间讲的太好了，简洁明了，学了这些之后大部分Lp的基本工具都有了。
后面的Fourier分析与广义函数是标准的内容，用很简洁的语言就解释明白了各个定义与定理证明。
大三下学期我去当了一次本科实变函数的助教，习题课上的补充内容大多也摘自Folland这本书，比如说L^p空间，比如说Fourier变换的性质，比如说收敛性的题目。
总之这本书的每一条定理、习题都有它自己的目的，如果认真刷下来，回头再看，会发现非常漂亮，尽管初读时会有所不适。
看这本书最好是学过本科的实变函数，并会一些泛函分析。这样的话上手很快。

干脆利落，零废话。并且深度对于“本硕贯通”而言，够。