# Kolmogorov & Fomin Textbooks

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).

• 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. – Stephen Montgomery-Smith Dec 2 '13 at 21:22
• 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. – Stephen Montgomery-Smith Dec 2 '13 at 22:17
• 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! – Self-teaching worker Oct 24 '14 at 16:02