书名】Introductory Real Analysis
【作者】by A. N. Kolmogorov (Author), S. V. Fomin (Author)
【出版社】Dover
【出版日期】1975
【文件格式】PDF
【页数】403
【ISBN出版号】0486612260
【资料类别】Real Analysis
【市面定价】10.85美元（Amazon Paperback）
【是否缺页】完整
【关键词】Real Analysis, Functional Analysis
【内容简介】Overall, this book is a very strong "introduction" (I use the word grudgingly, see below) to real analysis. Topics range from the basics of set theory through metrics, operators, and Lebesgue measures and integrals. Particularly well done are the section on linear maps and operators, which include excellent generalizations as well as the usual concrete examples. The book usually includes a large number of examples and exercises on each topic which aid in the understanding of the material (though in a few instances, most notably the introduction to measure, it would have been more helpful to have examples as the theory was being developed instead of spending 20 pages getting through the theorems and only then giving a few examples).

The main problem for this book, however, is that it is located at an awkward level in terms of its assumptions of what students have seen before. Most of the material covered is that of a first analysis course, and the book is probably usually used as such. The authors, however, sometimes make assumptions that students have had exposure to some of the concepts before, claiming that "the reader has probably already encountered the familiar Heine-Borel theorem", for example. One particularly annoying case was when the authors gave as an example that the set of polynomials with rational coefficients is dense in the set of continuous functions, and left it at that. Are we supposed to have encountered Weierstrass's theorem before we take our first analysis course