Customer Reviews (1)

Opinion on Measure and Integration by Sterling K. Berberian
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. ... Read more

Book Description
By generalizing the concept of point function to that of afunction ("soma" function ) over a Boolean ring,Carathéodory gives in this book an elegant algebraictreatment of measure and integration. This is the second Englishlanguage edition. ... Read more

Book Description
This digital document is an article from Atlantic Economic Journal, published by Atlantic Economic Society on March 1, 1996. The length of the article is 2789 words. The page length shown above is based on a typical 300-word page. The article is delivered in HTML format and is available in your Amazon.com Digital Locker immediately after purchase. You can view it with any web browser.

Citation Details
Title: The elasticity of substitution as a proxy measure of economic integration.
Author: George k. Zestos
Publication: Atlantic Economic Journal (Refereed)
Date: March 1, 1996
Publisher: Atlantic Economic Society
Volume: v24Issue: n1Page: p43(9)

Distributed by Thomson Gale ... Read more

Customer Reviews (1)

Excellent Treatise on the topic.
This book is well written and nicely layed out. With a great exposition and any worked examples, it is all you need for self study.And with plenty of problems, and solutions or hints to each, it is a great companionfor any first year graduate student in mathematics.The scope of the bookis limited to its title (measure and integration), but you will find it agreat reference for many years! ... Read more

Book Description
Although of unquestioned power and practical utility, the Lebesgue Theory of measure and integration tends to be avoided by mathematicians, due to the difficulty of obtaining detailed proofs of a few crucial theorems.In this concise and easy-to-read introduction, the author demonstrates that
the day-to-day skills gleaned from Legesgue Theory far outweigh the effort needed to master it. This compact account develops the theory as it applies to abstract spaces, describes its importance to differential and integral calculus, and shows how the theory can be applied to geometry, harmonic
analysis, and probability. Postgraduates in mathematics and science who need integration and measure theory as a working tool, as well as statisticians and other scientists, will find this practical work invaluable. ... Read more