Infinite Dimensional Analysis: A Hitchhiker’s Guide 3rd Edition by Charalambos D. Aliprantis (PDF)

Description

What you’ll find in this monograph is nothing less than a complete and rigorous study of modern functional analysis. It is intended for the student or researcher who could benefit from functional analytic methods, but who does not have an extensive background in the subject and does not plan to make a career as a functional analyst. It develops the topological structures in connection with a number of topic areas such as measure theory, convexity, and Banach lattices, as well as covering the analytic approach to Markov processes. Many of the results were previously available only in works scattered throughout the literature.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐I like this. This book is well-organized and includes almost everything which people should know to apply infinite dimensional space model. One bad thing is the lack of exercise problems.

⭐A great book.

⭐This book is recommended by Prof Marcus Berliant. I wish I know about this book much earlier. I really love it.

⭐Book came in poor condition, back cover bent

⭐I love this book ,….the other book of professor Aliprantis (Principles of Real Analysis) is excellent too!!

⭐This book has a large amount of content that is not stated with as general assumptions in any other book. The authors do not even tacitly assume that topological spaces are Hausdorff, and I like this because who knows where one might want to use the machinery that is developed. I think it is laughably unaware for a mathematician to complain about developing too much machinery or proving results in more generality than is needed in what they might call practice. Of course if this machinery is never used then it is frivolous, but by developing the right machinery and meticulously not identifying objects (i.e., not tacitly identifying spaces and their dual spaces or functions and elements of Lp spaces) we can avoid the confusion that often appears when doing technical proofs, merely at the cost of more notation and more machinery.The book has all the material on Banach spaces that is commonly taught in a course on functional analysis. It does not cover the spectral theorem or functional calculus, which I think is right, as to explain these properly takes a course entirely on them (or they can be explained poorly as part of a general graduate analysis course). It also has a chapter on convexity and subgradients which I thought was the best coverage I could find.What stands out the most is the presentation of measure theory in this book. The authors present various structures like algebras, rings, and semirings of sets, and although it is common only to speak of sigma-algebras, these are useful weaker structures that are worth becoming familiar with. For example, the Caratheodory extension theorem is cleanly stated using semirings of sets. Aliprantis and Border give what is probably the most structural proof that exists of the Kolmogorov extension theorem, even if it is long because it develops machinery so that nothing is ad-hoc.There is so much stuff in this book that I want to list it all (except the language of AM spaces, which I didn’t like but which can be read around). I can merely say that for anyone working on the intersection of functional analysis and measure theory or anyone who wants a measure theoretic presentation of results commonly thought of as part of probability theory, this book is the best that now exists and there are scarce places where it can be improved.

⭐I am a robotic engineer and I bought this book for modeling the infinite dimensional robot system. I read once and now I read it once again. This book truly extraordinary book, which span almost every analysis related topics such as topological space, metric space, measure space, correspondence space,… just name a few. And It is very well organized as a text book and a good reference. Even though the authors claimed that there is some missing contents such as differentiability, the book deserves five stars. If someone, who want to grasp a 17~21 century analysis, with a very readable and well-organized manner, this book is for you. Highly recommended!!!

⭐I’ve bought this book because I needed to quickly fill a lot of gaps in my mathematical knowledge. The chapter about correspondances is highly valuable because there are very few books about this topic. Compared to Berge’s Topological Spaces the treatment is much more simplified but the scope and audience is very different. While Berge goes to the pure mathematician this book is very useful for a standard “mathematical methods in economics and finance” or “mathematics for economists” course imparted in any university. Usually, that kind of course covers metric spaces, normed spaces, compact sets, convexity, kuhn-tucker theorem, correspondances, berge’s maximum theorem, linear spaces, separation theorems and fixed point theory which are very affordable in this book. Also my edition is a hardcover printing which makes it one of the most elegant books in my collection. As a reference book is very useful and a good complement to Efe A. Ok’s “Real Analysis With Economic Applications”.

⭐@Springer: The book is certainly good enough and probably expensive enough to warrant sewing. My copy is quickly disintegrating into an infinite pile of loose pages.

⭐Literally every part of math that an economist would ever want to know and more.

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