
 This highly flexible text is organized into two parts: Part I is suitable for a onesemester course at the firstyear graduate level, and the book as a whole is suitable for a fullyear course. Part I treats the theory of measure and integration over abstract measure spaces. Prerequisites are a familiarity with epsilondelta arguments and with the language of naive set theory (union, intersection, function). The fundamental theorems of the subject are derived from first principles, with details in full. Highlights include convergence theorems (monotone, dominated), completeness of classical function spaces (RieszFischer theorem), product measures (Fubini's theorem), and signed measures (RadonNikodym theorem). Part II is more specialized; it includes regular measures on locally compact spaces, the RieszMarkoff theorem on the measuretheoretic representation of positive linear forms, and Haar measure on a locally compact group. The group algebra of a locally compact group is constructed in the last chapter, by an especially transparent method that minimizes measuretheoretic difficulties. Prerequisites for Part II include Part I plus a course in general topology. To quote from the Preface: "Finally, I am under no illusions as to originality, for the subject of measure theory is an old one which has been worked over by many experts. My contribution can only be in selection, arrangement, and emphasis. I am deeply indebted to Paul R. Halmos, from whose textbook I first studied measure theory; I hope that these pages may reflect their debt to his book without seeming to be almost everywhere equal to it." Request an examination or desk copy. Readership Graduate students interested in teaching and learning the theory of measure and integration. Table of Contents



AMS Home 
Comments: webmaster@ams.org © Copyright 2014, American Mathematical Society Privacy Statement 