Real Analysis: Theory Of Measure And Integration (2Nd Edition) by James J Yeh (PDF)

Description

This book presents a unified treatise of the theory of measure and integration. In the setting of a general measure space, every concept is defined precisely and every theorem is presented with a clear and complete proof with all the relevant details. Counter-examples are provided to show that certain conditions in the hypothesis of a theorem cannot be simply dropped.The dependence of a theorem on earlier theorems is explicitly indicated in the proof, not only to facilitate reading but also to delineate the structure of the theory. The precision and clarity of presentation make the book an ideal textbook for a graduate course in real analysis while the wealth of topics treated also make the book a valuable reference work for mathematicians.

User’s Reviews

Editorial Reviews: Review I recommend this book for a student who is helped by a good adviser — Mathematical Reviews “Mathematical Reviews””Every concept is defined precisely and every theorem is presented with a detailed and complete proof. Counter-examples are presented to show that certain conditions in the hypothesis of a theorem cannot be simply dropped.”

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

⭐Great book for graduate students in statistics and electrical engineering. Author provides a good set of topics written in an accessible manner, including explicit proofs. In an ideal world on would get to spend a year studying this book before taking a measure theoretic probability course. It would be difficult to beat this book in general, and for the price it is even tougher. An alternative, which is a shorter book but contains some different topics of particular interest in probability, is “Measure Theory” by Donald L. Cohn. I don’t know if I could recommend one over the other, but if you were to buy two books, these are probably the two you want.

⭐This book is based on the author’s lectures on real analysis at UC Irvine. I attended those lectures in the late 1990s. The book follows the class notes closely. The material is presented logically and very carefully. All theorems etc are carefully presented and proved, and there are few (if any) errors. Simply put, this is a great book from which to learn measure and integration theory.

⭐The book is excellent. This is a graduate text and contains a lot of materials. At the same time it is easy to follow the proofs. Contrary to some graduate text, it is not full of “it is easy to see” that takes hours to figure out…

⭐I started learning measure theory this semester and bought several books on the matter. This one rose to the top very quickly . It is very clear and very thorough. It’s become one of two books I use to learn the subject(the other book is Bartle’s Measure and Integration.)

⭐This book covers a lot of material on measure and integration and the author wrote certainly one of the most solicitous book in this subject.Over 700 pages long, this book will surely cover all the contents of a classical course on measure and integration theory. All explanations and proofs are written in a highly didactical way. This means that the author did not care much about conciseness, and took a great amount of work by choosing good notations and developing his arguments caring with the student understanding in mind. Other books on the subjects are mostly too concise in their explanations or do not cover too many topics or ,wrose, are not written with the sufficient care to be called a didactic book.The result is a elegant, encyclopedic and useful book on understanding the basics of measure and integration.

⭐Measure Theory is not an easy subject. I have tried a few books and journals and it has proved difficult to penetrate. However, with this book, I am finally getting to understand the concepts. I particularly like the examples as they actually help bring the points home. I hope the author can consider writing more books on the subject. I would definitely recommend this book to anyone who is trying to understand Measure Theory. The book gets my five stars. The only thing that could be improved is the binding. The publisher should consider doing a better paperback or a good hardcover.

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