General Theory of Functions and Integration

I have many friends who are graduate students or upper level undergrads in mathematics at Columbia and Yale who are suffering in their Real Variables courses because their arrogant,aloof instructors are using overpriced,ultra-TERSE higher analysis texts like Rudin's Real And Complex Analysis or Royden's incomprehensibly "classic" text.(For those of you who are using Royden and spent the insane cover price on it,you should realize there are a TON of errors in it.)I feel so bad for them because they really got taken for a ride-for a fraction of the cost,they could have had this GEM of a text.Taylor,famous for his Advanced Calculus,developed this text as a series of lecture notes at UCLA in the 1950's.Taylor rightly realizes the key to understanding mathematical analysis/measure theory at this level is a firm grip of point-set theory and abstract topological spaces-of which the real and complex numbers systems are but special cases.He then proceeds to develop the metric and topological properties of the number systems in this abstract setting-focusing on the rigorous set-theoretic foundations. Critical to analysis(and pure math in general) are PRECISE DEFINITIONS-and this is what makes Taylor's approach to the subject so beautiful and crystal clear,without sacrificing rigor or exposition of challenging theories.How many analysis text do you know develop BOTH the classical Lesbegue approach to modern integration as well as the Daniell approach for functional analysis-without losing an ounce of clarity? Run-don't-walk to your bookstore and order this if you're in upper level analysis courses. This will become a standard reference throughout you're career-I promise.