Real Analysis: Measure Theory, Integration, and Hilbert Spaces (Princeton Lectures in Analysis Book 3) by Elias M. Stein (PDF)

Description

Real Analysis is the third volume in the Princeton Lectures in Analysis, a series of four textbooks that aim to present, in an integrated manner, the core areas of analysis. Here the focus is on the development of measure and integration theory, differentiation and integration, Hilbert spaces, and Hausdorff measure and fractals. This book reflects the objective of the series as a whole: to make plain the organic unity that exists between the various parts of the subject, and to illustrate the wide applicability of ideas of analysis to other fields of mathematics and science. After setting forth the basic facts of measure theory, Lebesgue integration, and differentiation on Euclidian spaces, the authors move to the elements of Hilbert space, via the L2 theory. They next present basic illustrations of these concepts from Fourier analysis, partial differential equations, and complex analysis. The final part of the book introduces the reader to the fascinating subject of fractional-dimensional sets, including Hausdorff measure, self-replicating sets, space-filling curves, and Besicovitch sets. Each chapter has a series of exercises, from the relatively easy to the more complex, that are tied directly to the text. A substantial number of hints encourage the reader to take on even the more challenging exercises. As with the other volumes in the series, Real Analysis is accessible to students interested in such diverse disciplines as mathematics, physics, engineering, and finance, at both the undergraduate and graduate levels. Also available, the first two volumes in the Princeton Lectures in Analysis:

User’s Reviews

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

⭐This book is the best book on real analysis I have ever studied. It does a wonderful job in bridging undergraduate level with graduate level analysis. I have not seen any book that makes measure and Lebesgue theory so easy to understand.The books begins by defining what a “measure” is all about. And the description is so intuitive and geometrical that you would wonder why you weren’t taught it this way before. The book then goes into Lebesgue theory and all of it suddenly becomes so easy.The book has plenty of wonderful examples and a good set of over 30 problems per chapter.Elias Stein (one of the authors) is a very renowned mathematician, and one need not worry about the accuracy of the proofs in the book–they are “bullet-proof”, and at the same time succinct.If you are struggling with W. Rudin’s book on Analysis, this book is a MUST for you.

⭐A masterpiece by Stein. This is a book that everyone who’s interested in measure theory must read. Very on point, very clear, and well written. Goes over all you need to do research or even if you’re a graduate student. Not a very advanced book but talk about whatever you need to understand advanced research areas in mathematics, statistics, and even electrical engineering. Very great book.

⭐There are some typos and errors scattered throughout the text.This gives a very quick introduction of Lebesgue measure & integration and differentiation theory. The rest is applications.Real Analysis by Royden & Fitzpatrick has a more thorough introduction to not just Lebesgue but also abstract measure theory. It also has more topics leading to functional analysis.The book was in good condition.

⭐This book is very nice, concise and still clear to read. I still did not do a lot into it (only chapter one so far).I taken a course in Analysis before and decided to read this book just to review and to study the subject through a different perspective.

⭐The book was delivered fast.The book was in cool condition.The title of the book was Real Analysis: Measure Theory, Integration, and Hilbert Spaces (Princeton Lectures in Analysis) (Bk. 3).

⭐a good textbook

⭐Very useful book in very good conditions

⭐This book is written ok. However, I used this for a graduate level measure theory course and it was not in depth enough.

⭐This is an excellent book on Measure theory and integration. The authors give proper motivation for the introduction of certain concepts. Its well written, but a bit advanced level book.

⭐Must by

⭐Excellent book

⭐Excellent

⭐Book is a gem. Would recommend any student of math to read it.

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