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图书翻译质量问题恐怕在全世界都存在，以下评论引自Amazon，关于Introductory Real Analysis,该书作者是Kolmogorov和Fomin，翻译者(或者叫编辑者）Richard Silverman.
36 of 36 people found the following review helpful:
Are all Silverman's "translations" like this one?, May 26, 2004Reviewer: A reader
First, let us be precise in reviewing this book. It is NOT a book by Kolmogorov/Fomin, but rather an edited version by Silverman. So, if you read the first lines in the Editor's Preface, it states, "The present course is a freely revised and restyled version of ... the Russian original". Further down it continues, "...As in the other volumes of this series, I have not hesitated to make a number of pedagogical and mathematical improvements that occurred to me...". Read it as a big red warning flag. Alas, I would have to agree with the reader from Rio de Janeiro. I've been working through this book to rehash my knowledge of measure theory and Lebesgue integration as a prerequisite for stochastic calculus. And I've encountered many results of "mathematical improvements" that occurred to the esteemed "translator". Things are fine when topics/theorems are not too sophisticated (I guess not much room for "improvements"). Not so when you work through some more subtle proofs. Most mistakes I discovered are relatively easy to rectify (and I'm ignoring typos). But the latest is rather egregious. The proof of theorem 1 from ch. 9 (p.344-345) (about the Hahn decomposition induced on X by a signed measure F) contains such a blatant error, I am very hard pressed to believe it comes from the original. That book survived generations of math students at Moscow State, and believe me, they would go through each letter of the proofs. Astounded by such an obvious nonsense, I grabed the only other reference book on the subject I had at hand, "Measure Theory" by Halmos. The equivalent there is theorem A, sec. 29 (p.121 of Springer-Verlag edition), which has a correct proof.
For those interested in details, Silverman's proof states that positive integers are strictly ordered: k1<k2<...<kn<... which is nonsense. Consider subsets B1 and B2 such that F(B1)=3, F(B2)=2, for example. That gives you both k1=k2=1. The flaw of course is not in this slip-up per se, but rather in the logic of the proof which follows from the above ordering of k's. Compare vs Halmos text to see the difference. It may seem insignificant to certain translators, but in mathematics, out of all of sciences, subtle details change an elegant proof to a flagrant nonsense.
Unfortunately, I don't have the Russian original. Instead, I'm trying to get the other, hopefully real translation, "Elements of the Theory of Functions and Functional Analysis". BTW, this is the actual title of the original, not "Introductory Real Analysis". Which apparently is causing significant confussion amoung past and present readers. To give you a background info, the Russian original is (or has been, at least) used as a textbook for a third-year subject for (hard-core) math students. Meaning, in the preceding two years they would complete a pre-requisite four-semester calculus course. For example, criteria of convergence of series and their properties is an assumed knowledge in presentation of Lebesgue integral. So, I think most of the critique from earlier reivews is a bit misdirected. The original book is a great starting book into functional analyis/Lebesgue integration and differentiation, but proofs require solid understanding of fundamentals of calculus.
The best part about Kolmogorov's text is the clarity of conceptual structure of the presented subject a reader would gain, if he/she puts some effort. You would gain a thorough understanding, not just a knowledge of the subject. There is quite a difference between the two, and not that many authors succeed in delivering that.
But to gain that from Kolmogorov, I would suggest the other, "unimproved" but real, translation.
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