

Amazon.com: Measure Theory (Graduate Texts in Mathematics): Books: Paul R. Halmos (Site not responding. Last check: 20071107) 
  This book is an overview of measure theory that is somewhat dated in terms of the presentation, but could still be read profitably by someone interested in studying the subject with greater generality than more modern texts. 
  Indeed, the author does an excellent job in presenting measure theory in its entire generality semirings, rings, hereditary rings, algebras, sigma algebras and their extensions are all considered in detail, as well as measures on these set systems: finitely additive, sigma additive, inner measures, outer measures, sigmafinite measures, the completion of measures, regular measures). 
  My impression of measure theory has gone from seeing it as abstract mathematical machinery for simplifying analysis proofs, to a kind of mathematical philosophy that unifies the infinite with the discrete, and lays the proper foundations for inference, probabilistic reasoning, and learning; i.e. 
 www.amazon.com /MeasureTheoryGraduateTextsMathematics/dp/0387900888 (1726 words) 
