Measure and Integration (Chelsea Publications), by Sterling K. Berberian


Download PDF Measure and Integration (Chelsea Publications), by Sterling K. Berberian

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Measure and Integration (Chelsea Publications), by Sterling K. Berberian

Measure and Integration (Chelsea Publications), by Sterling K. Berberian

Measure and Integration (Chelsea Publications), by Sterling K. Berberian

Download PDF Measure and Integration (Chelsea Publications), by Sterling K. Berberian

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Measure and Integration (Chelsea Publications), by Sterling K. Berberian

This highly flexible text is organized into two parts: Part I is suitable for a one-semester course at the first-year graduate level, and the book as a whole is suitable for a full-year course. Part I treats the theory of measure and integration over abstract measure spaces. Prerequisites are a familiarity with epsilon-delta 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 (Riesz-Fischer theorem), product measures (Fubini’s theorem), and signed measures (Radon-Nikodym theorem). Part II is more specialized; it includes regular measures on locally compact spaces, the Riesz-Markoff theorem on the measure-theoretic 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 measure-theoretic 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.”

  • Sales Rank: #2366365 in Books
  • Published on: 2011-03-09
  • Original language: English
  • Dimensions: 9.00″ h x 6.25″ w x .75″ l, 1.25 pounds
  • Binding: Hardcover
  • 312 pages

Most helpful customer reviews

11 of 13 people found the following review helpful.
Opinion on Measure and Integration by Sterling K. Berberian
By ADENIYI GRILLO
Once upon a time I was once told, the student of mathematics, in the initial stages of his career is given Abstract Algebra, Mathematical Analysis and Point Set/General Topology from which nothing follows. Well, presenting a student these branches that way is like giving one incomplete jigsaw puzzles and asking him to put them altogether. This was my favorite book on Measure Theory & Integration of which I preferred to Paul Halmos’s classic on the similar subject in my undergraduate years. The treatment is very abstract, but if the reader purses for a moment, one starts to see some form of unification and connection running throughout the whole spectrum of Mathematics (Pure/Applied)as far Intergration is concern. The treatment is of course the generalization of the Riemman/Riemman Stieltjes integrals. This then makes one belief that integration is not only done on the real line, but also on more abstract spaces as well(generalization of the real/complex number system). The book explains the how/why as to the justification of the application of integrals to Mathematical Statistics (Probability Theory), Engineering and the other areas of the Mathematical Sciences. The basis of my review is not based on chapter by chapter, but as to the reason why such a book was written in the first place. Usually one takes a course in elementary Calculus thinking it all ends there, but that is not the end of the story. I believe after reading classic text like T.M. Apostol’s Mathematical Analysis, Walter Rudin’s Principles Of Mathematical Analysis and Royden’s Real Analysis, I think Sterling K. Berberian’s book should then be read and be placed on every mathematician’s bookshelf to explain why we human beings enjoy performing Integration in the first place. All the Theorems and Proofs are nicely written, and the treatment which of course is based on Set Theory is very good. I will recommend this book to every mathematician doing research.

1 of 1 people found the following review helpful.
Thorough and eloquently written–a pearl of mathematical discourse.
By Matthew Maycock
This is probably one of the best books I’ve read. It’s wonderfully written and easy to follow (although I reread some parts just because of the depth of the material). Reading it readily prepared me for a class on the subject.

My mother bought this for me as a present. I liked it so much I bought a copy for a friend so that I could review it. This is really an amazing text.

See all 2 customer reviews…

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