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. Self-contained and comprehensive, this elementary introduction to real and functional analysis is readily accessible to those with background in advanced. The first four chapters present basic concepts and introductory principles in or for the classroom — it is basic one-year course in real analysis.
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Your input will be greatly appreciated. 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 This is probably the kologorov text you are referring to.
Introductory Real Analysis
The first text you are talking about is the “translation” by Silverman of the second Russian edition. I write “translation”, because the translator states: 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 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.
Introductory Real Analysis – A. N. Kolmogorov, S. V. Fomin – Google Books
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. If any amalysis 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 kolmovorov a wonderful science as analysis is! 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. It may be the case that some of these are of later editions. 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.
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