Lebesgue Integration and Measure

Its a very good text for a first meeting on Lebesgue integration, measure and functional analysis. Rigorous, elegant and simple. A quality book for pure and applied mathematics.However I found two little mistakes:In page 151, in the proof of the integral of a transformation, he makes use of the Dominated Convergence Theorem two times (one first time, at the begining of page 151, is right). Thats wrong because we can't "dominate" the function "g" when K -> inf. The correct proof involves divide the function in positive and negative parts and then aplicate Monotone Convergence Theorem. The same in the end of the proof when he generalizes to infinite measure sets.<p>In page 157, equation (7) should be verified when ||h||<2*delta, not ||h||<delta as he writes. This is to assure that the set C+ is contained in that region.<p>Anyway, a brilliant text. Purchase it.

I picked up this book on a trip to London. I've known some complex analysis and real analysis, and I decided to learn some Lebesgue on my own; ergo the purchase of this book. The style of writing is very lucid: quite informal at times, and the math part is really well-presented (the explanation on 'measure zero' set, for example, is clear, and mathematically rigorous). The topics chosen are not in-depth (I learnt much more on the topic during an actual course in college), but the book definitely works well as a supplement reading, when you are taking real analysis course.