Tao T. Analysis II

Hindustan Book Agency, 2006. - 272 pages.This book (as well as the 1st volume) comes out from the author's lecture notes. It's decent work but I would expect much more from a renowned mathematician.The book takes a very formal approach. It starts with building the number systems, from natural numbers to real numbers. The proofs are generally more detailed than similar text books. The chapters on Lebesgue integration are good. The author explains why the Lebesgue measure exists, instead of just presenting the definitions and theorems, like most introductory books do. The remarks dotted everywhere are instructive, reflecting the author's broad knowledge in mathematics. No surprise, given Tao is one of the most versatile mathematicians in our time.