Russian Equivalent of Big Rudin Is there any Russian-authored textbook on Analysis equivalent to Big Rudin (Real and Complex Analysis)?
I like Russian math textbooks a lot. I am looking for Russian textbooks (either in English or Russian, preferably English) in analysis covering the same material as "Principles of Mathematical Analysis", "Real and Complex Analysis" and "Functional Analysis" by Rudin.
 A: My teachers suggested Real Analysis: Measures, Integrals and Applications by Makarov and Podkorytov and Lectures And Exercises on Functional Analysis by Helemskii when I had those courses. There is a 2nd edition of Helemskii available in russian. 
A: I can highly recommend Grigorii M. Fichtenholz's books, they are very instructive for students. 
I am not sure about the English title or Russian Original Title, the German versions are called
Differential- und Integralrechnung. I,II,III.
This is a classical textbook. The topics are more basic (series, integration....), not covering the functional analysis of Rudin.
See this link in MathSciNet for some of his books: http://www.ams.org/mathscinet-getitem?mr=84531
A: There is no Russian equivalent of these books, like there is no equivalent of "baby Rudin" (which they translated). But one can certainly cover the same material with several books available in Russian (some of them translated into Russian). Some of these books are mentioned in other answers. 
EDIT. I suspect that absence of equivalent books is due to the difference of education systems. Undergraduate education in Soviet Union was much more advanced then undergraduate education in the US. For example Kolmogorov-Fomin, and Shilov, and Helemski mentioned in the other answers are undergraduate textbooks. (Normally such courses of Complex and Functional analysis are taught on the 3-d year of undergraduate studies).
A student who completed undergraduate education and enrolled to a
graduate pprogram is expected to begin his/her research immediately.
So there is no such thing as a "graduate text in Complex Analysis" in Russian. Graduate education will be much more focused (on some particular topic in Complex Analysis), and the student will be expected to read original papers and monographs, rather than a textbook. 
A: A classic is Kolmogorov and Fomin's Elements of the Theory of Functions and Functional Analysis, also published (in a revised version) under the title Introductory Real Analysis. (Amazon presents them as distinct books, but they are really based on the same Russian text.) From a somewhat less distinguished author there is also G.E. Shilov, Elementary Real and Complex Analysis.
A: A good choice he would be the two-volume textbook of Vladimir Zorich: Mathematical Analysis which is available in English now in its second edition. See http://www.springer.com/gp/book/9783662487907 and http://www.springer.com/gp/book/9783662489918 . The books are available in German, too. 
A: Functional analysis: S. S. Kutateladze Fundamentals of Functional Analysis
Complex analysis: Yu. V. Sidorov, M. V. Fedoryuk, M. I. Shabunin Lectures On The Theory Of Functions Of A Complex Variable
Elements of Fourier analysis: N. I. Akhiezer Lectures on Integral Transforms
