Elements of the Theory of Functions and Functional Analysis [Two Volumes in One] Paperback – 8 May 2012

Good book

This is a classic and just what I wanted. I just don't know how Kolmogorov managed to get so much material/content into so little space and yet write so succinctly, clearlyand smoothly - result: an easily, readable book which makes difficult material accessible

A classical treatment of functions and space.

As a text that manages to get so much material covered in such little space, as the work of one of the greatest mathematicians of all time, as a lesson in how to write beautiful proofs, this is a 5-star. As a first introduction to Functional Analysis, this is too dense. You are better off using one of the more popular recent texts or perhaps even Shilov whose own Functional Analysis may have been based on this (though only its first chapter which seems equivalent to the first book here).The first chapter on Sets reads very smoothly and elegantly sums up material you are likely to be quite familiar with. Then you plunge into topology (mostly metric spaces, actually) which is overall very well covered, though you might want to use a gentler introduction to that such as the Oxford University Press title by Sutherland (not strictly necessary if you're willing to devote some time to this). The next chapter - on normed linear spaces - is maybe a little too thin - here you may want some other Banach space textbook supplement. After some material on spectral theory and related areas, you find yourself in the second book which kicks off with Measure Theory and includes Hilbert Spaces. I was primarily interested in the first book so only browsed through parts of the second and can't therefore comment on those here.I agree with the otehr reviewer that this is a better image of the text than the Dover is (and a slightly larger book) but they're the same book.As a refresher after some absence, this book will serve you very well. I will return to measure theory at some point and cover the second book, given that this is by the master who virtually founded the modern theory of probability, but for now I can recommend the first book heartily to anyone who has had some exposure to functional analysis.

Sadly, I didn't value this book. It's surrealistic and full of nonsense pretending superior class of advance.Maybe it has few approved points within, definitely only some simple and intuitive things lifted to the rank of impossible to understand complexity, meaning something "unachievable for usual John Smith".You'll surely carry much more from lessons and seminars and the material is not anything too difficult even for elementary school students. If only expressed in conventional mathematical formulas, instead of surrealistic setup of random mathematical symbols.