Measure, Integration & Real Analysis (Graduate Texts in Mathematics Book 282) by Sheldon Axler (PDF)

Description

This open access textbook welcomes students into the fundamental theory of measure, integration, and real analysis. Focusing on an accessible approach, Axler lays the foundations for further study by promoting a deep understanding of key results. Content is carefully curated to suit a single course, or two-semester sequence of courses, creating a versatile entry point for graduate studies in all areas of pure and applied mathematics.Motivated by a brief review of Riemann integration and its deficiencies, the text begins by immersing students in the concepts of measure and integration. Lebesgue measure and abstract measures are developed together, with each providing key insight into the main ideas of the other approach. Lebesgue integration links into results such as the Lebesgue Differentiation Theorem. The development of products of abstract measures leads to Lebesgue measure on Rn.Chapters on Banach spaces, Lp spaces, and Hilbert spaces showcase major results such as the Hahn–Banach Theorem, Hölder’s Inequality, and the Riesz Representation Theorem. An in-depth study of linear maps on Hilbert spaces culminates in the Spectral Theorem and Singular Value Decomposition for compact operators, with an optional interlude in real and complex measures. Building on the Hilbert space material, a chapter on Fourier analysis provides an invaluable introduction to Fourier series and the Fourier transform. The final chapter offers a taste of probability.Extensively class tested at multiple universities and written by an award-winning mathematical expositor, Measure, Integration & Real Analysis is an ideal resource for students at the start of their journey into graduate mathematics. A prerequisite of elementary undergraduate real analysis is assumed; students and instructors looking to reinforce these ideas will appreciate the electronic Supplement for Measure, Integration & Real Analysis that is freely available online.

User’s Reviews

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

⭐This review is for the supplement, NOT the main text. (Although I wish he would’ve included the supplement into the main text as it would’ve only added about 40 pages.)I think the supplement is OK. I think it’s a very nice start, but many proofs require (in my opinion) slight detail to finish selling the point. Obviously you should know how to proof, everything about functions, etc. before picking this book, and even the supplement up. I’m sure the text is fine, as I’ve read part of his book on Linear Algebra and that book has been great. Also solutions and hints would have been great to have. At least to half!

⭐The author has done an excellent job of exposition and proofs making this a very readable book. Once started I had a hard time putting the book down. Key points are highlighted in yellow or blue, yellow for definitions and blue for propositions or theorems. The book is packed with proofs of results and in some cases these are counter examples of previous theorems where the hypotheses have been weakened. I already had some familiarity with measure theory but the book provides a reference for the results and the proofs. These results are of course very important in that they all have applications in mathematical physics. This book goes beyond the main results of measure theory including some results on Functional Analysis, Spectral Theory and Fourier Analysis. It does not attempt to go into topics too advanced and again this makes the book very readable as it means that the reader will get a feeling that he or she really understands the topic after reading the proofs. I recommend this book very highly for anyone interested in Measure Theory & Real Analysis.

⭐Stay away from this book unless you want to get addicted to beautifully written math textbooks. This book is right up the alley of “Linear Algebra Done Right” — beautifully written, amazing for self-study (I’m self-studying and sometimes it’s hard to put the book down), and leaves you wanting for more.Don’t get me wrong — it’s by no means an easy text. But it keeps everything interesting and motivated, the proofs are clear and very well written, and there are enough (at least for me) end of chapter exercises to keep everyone happy and drive home the key ideas from the associated chapters.All in all, among my favorites. Will be on the look out for more from Dr. Axler. (I hope he can write a text on functional analysis next!)

⭐This is an excellent reference and textbook on measure theory and real analysis. The book is intended for someone with a background in undergraduate or first year graduate analysis such as Walter Rudin’s mathematical analysis. The book can be read and understood by anyone with a good solid background in mathematics.

⭐Delivered early but book was not well cushioned resulting in dents at the corners

⭐I like the book. It is easy to read and has good printing quality with colorful pictures. But the price is high.

⭐This has to be the best introduction to measure theory around, and free too. The text is clear and interesting at all times. It puts my lectures at Oxford in the 60s to shame, the approach was contorted and diabolical!The book covers measure, Borel sets, integration and Fourier Transforms, and touches finally on orobability.If you read one book on this subject, read this one!

⭐Compact but very readable, rigorous but friendly. It’s hard to find books on measure theory or spectral theory that don’t require a lot of time. This book does a lot in 400 pages, but they’re all quite readable and flow well. At the end you’ll have done the spectral theory of compact operators with 100% rigour.It summarised nicely pretty much all the analysis of my undergrad maths degree, excluding complex analysis.It’s not quite the pedagogical masterpiece of Axler’s Linear Algebra Done Right, but it’s an even, straight path to walk on.

⭐The review is not about the content.The preface mentions defns and theorems in yellow and blue boxes in print version.However Print copy is black/ white. Not sure if this is original. You pay for a hardbound expensive copy expecting good visual experience but are left disappointed!!

⭐The content of the book is, of course, excellent. The printing is extremely poor though, with ink bleeding, streaks of fuzzy printing, and very flimsy paper.edit: I’ve since received a properly printed version, and it is beautiful. In case you get a copy with mediocre printing quality (especially if you see signs that it is printed on demand), I highly encourage you to bring it up with Springer. To avoid getting unauthorized print-on-demand copies, I also recommend to purchase directly from Springer.

⭐It’s a really good book but the lack of solutions to problems is a major, deliberate, and needless obstacle to self-learners and students.

Keywords

Free Download Measure, Integration & Real Analysis (Graduate Texts in Mathematics Book 282) in PDF format
Measure, Integration & Real Analysis (Graduate Texts in Mathematics Book 282) PDF Free Download
Download Measure, Integration & Real Analysis (Graduate Texts in Mathematics Book 282) 2020 PDF Free
Measure, Integration & Real Analysis (Graduate Texts in Mathematics Book 282) 2020 PDF Free Download
Download Measure, Integration & Real Analysis (Graduate Texts in Mathematics Book 282) PDF
Free Download Ebook Measure, Integration & Real Analysis (Graduate Texts in Mathematics Book 282)