There is nothing else remotely similar to it in any of the current books on integration, real analysis, set theory, or any other related subject. It is colossal, invigorating and refreshingly contemporary in its concerns. ... All in all, this book reaffirms for us how subtle, beautiful and joyous mathematics can be.The Society for Industrial and Applied Mathematics has made available the entire review section -- i.e., that review together with the other reviews that were published with it -- on a web page maintained by SIAM. The review section is offered in several formats -- ps, pdf, dvi -- but the files are quite large. I am posting my book's review by itself as a dvi file (37 kilobytes), or as a web page, by permission of SIAM.
... extraordinary presence ... writes exceedingly well ... pace is measured, zealously well motivated, armed with historical observations, and often delightfully colloquial ...
Physically, the book is beautiful, with wide pages, impeccable design, striking binding, and gorgeous mathematical typesetting.
George L. Cain, Georgia Institute of Technology
This is quite a book! From the table of contents, it would appear to include just about everything one would want to know about the foundations of analysis. It is well-organized and the exposition in the sample chapters is quite good: clear, concise, and relatively easy to read. It is very good technically; the author knows what he is talking about.
Robert G. Bartle, Eastern Michigan University
At the very outset, I would like to say that I am *very much impressed* by what I have seen. I have read the Preface and understood the author's purpose and his aims. I admire him for his courage in attempting such a daunting task, and I admire him even more for what appears to me to be a very successful completion of this task. ... I am very excited over the prospect of this book being made available; it will be a *very useful* reference not only for beginning graduate students, but also for their teachers.
I find something magical just about on every page. So much information in a single book in a format so well suited for individual study ...
I must say, it is a damn good book! I have never encountered an analysis book before that is so interesting to read. I keep putting it back on the shelf because I'm supposed to be meeting some other commitments but then I keep taking it down and reading some more!
Dunford and Schwartz is something else entirely; and yet, there is enough likeness for a comparison to be of interest. The last two chapters of Volume I [DS] already go beyond HAF ... But the first twenty chapters of HAF correspond mostly to nothing in [DS]; some of this is prerequisite material which Dunford and Schwartz assumed known, but much of it is an introduction to a wider world.It is a mixed review, describing both virtues and flaws of my book -- e.g., the book is called "lively" and "effervescent," but some chapters are called "inadequate." Isbell mentions my discussions of constructivism, but he seems not to share my excitement about that topic. The review concludes favorably:
This book will be a valuable resource for the ambitious students at whom it is aimed and for a number of licensed mathematicians, outside analysis and perhaps inside, who are interested in broadening their perspectives. We are all in the author's debt.Isbell's whole review is available on-line.
However, this interweaving does not preclude skipping around in the book and reading small portions of it; I put in plenty of cross-references to facilitate that. If you want to read just part of my book, you won't have difficulty finding the other parts of the book that you need as prerequisites. And those prerequisites *are* in the book; you don't need to have a stack of other books by your side in order to read mine. Thus, for the beginner, my book has the advantage of being more self-contained than most ordinary graduate textbooks.