Customer Reviews

Measure and Integration.

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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.