There are two books by Kolmogorov & Fomin that I am interested in purchasing, namely Introductory Real Analysis and Elements of the Theory of Functions and Functional Analysis. Now, this will be my third book on graduate analysis; in particular, I have studied from Bartle’s Elements of Integration (which develops measure theory in an axiomatic/general sort of way) and a delightful little book called Introduction to Lebesgue Measure and Fourier Series by authors Wilcox and Myers (which develops the idea of Lebesgue measurable sets of the closed interval $[0,1]$, Lebesgue outer measure, and the Lebesgue integral). Next year, I will be starting graduate school; and, it appears that I will be using Royden or Rudin’s Real/Complex Analysis (but most likely Royden). As such, I am looking for one more text to tie everything together. So, I suppose my questions are as follows:

(1) Which of the two Kolmogorov & Fomin texts is better suitable for self-study?

(2) Which of the two Kolmogorov & Fomin texts contains topics most closely in line with the Royden text?

Thank you! Your input will be greatly appreciated. Note: I am also open to other suggestions assuming the cost of the text is low (or Frank Jones’s Lebesgue Measure on Euclidean Spaces would be an option).

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    $\begingroup$ I self taught myself using "Introductory Real Analysis." I remember it being a well written book, and easy to follow. It was only years later I learned that Kolmogorov was a super-genius. $\endgroup$ – Stephen Montgomery-Smith Dec 2 '13 at 21:22
  • $\begingroup$ Also, I don't think Rudin's book "Real and Complex Analysis" is a good book to start learning the subject. It is a great second book. He does everything in a slightly strange way, which is great when looking at the subject the second time. $\endgroup$ – Stephen Montgomery-Smith Dec 2 '13 at 22:17
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    $\begingroup$ If any user of those texts browses my questions, (s)he can find several points that I have found quite difficult in Kolmogorov and Fomin's "Elements of the Theory of Functions and Functional Analysis" (I am currently using an Italian language translation and "grasshopping" in the Russian original and its English translations, of which "Introductory Real Analysis" is a partial one). Enjoy your study of such a wonderful science as analysis is! $\endgroup$ – Self-teaching worker Oct 24 '14 at 16:02

Kolmogorov and Fomin wrote only one book. First it was published as two volumes under the name "Elements of the Theory of Functions and Functional Analysis", in 1954. This is probably the second text you are referring to. The first text you are talking about is the "translation" by Silverman of the second Russian edition. I write "translation", because the translator states: "The present course is a freely revised and restyled version of ... the Russian original...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..." So this is not a book by Kolmogorov and Fomin per se, and they never titled their work "Introductory real analysis". After that there were a third and fourth editions of this classical book in Russian, with a lot of material added. If you can read Russian, I would suggest to pick the latest edition. If not, my advice would be to choose another introductory text in analysis.

  • $\begingroup$ The French translation is based on the third Russian edition, which is almost identical to later editions, except for a section on the implicit function theorem added in the fourth edition. According to the preface to the sixth edition, there have been translations into English, Japanese, German, Czech, Hungarian, French, Spanish and Dari Persian. It may be the case that some of these are of later editions. $\endgroup$ – user49640 Mar 21 '17 at 5:40
  • $\begingroup$ It seems that all English translations are of the first or second editions. It is puzzling that no translations of the later editions are available. Does the third Russian edition differ much from the second one? $\endgroup$ – user0347284 Feb 23 '18 at 22:34
  • $\begingroup$ MIR-Moscow (Nauka-Moskba), the former soviet editorial house now defunct, published the book in several languages. The Spanish translation is based on the second edition of the book (1975). It was much more material than the two English translations that were based on the first edition. The Spanish translation is available on line in the Genesys Library. $\endgroup$ – Oliver Diaz Jun 23 at 22:29

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