Measures, Integrals and Martingales 2nd Edition by René L. Schilling (PDF)

Description

A concise yet elementary introduction to measure and integration theory, which are vital in many areas of mathematics, including analysis, probability, mathematical physics and finance. In this highly successful textbook, core ideas of measure and integration are explored, and martingales are used to develop the theory further. Other topics are also covered such as Jacobi’s transformation theorem, the Radon–Nikodym theorem, differentiation of measures and Hardy–Littlewood maximal functions. In this second edition, readers will find newly added chapters on Hausdorff measures, Fourier analysis, vague convergence and classical proofs of Radon–Nikodym and Riesz representation theorems. All proofs are carefully worked out to ensure full understanding of the material and its background. Requiring few prerequisites, this book is suitable for undergraduate lecture courses or self-study. Numerous illustrations and over 400 exercises help to consolidate and broaden knowledge. Full solutions to all exercises are available on the author’s webpage at www.motapa.de. This book forms a sister volume to René Schilling’s other book Counterexamples in Measure and Integration (www.cambridge.org/9781009001625).

User’s Reviews

Editorial Reviews: Review Review of previous edition: ‘… thorough introduction to a wide variety of first-year graduate-level topics in analysis … accessible to anyone with a strong undergraduate background in calculus, linear algebra and real analysis.’ Zentralblatt MATHReview of previous edition: ‘The author truly covers a wide range of topics … Proofs are written in a very organized and detailed manner … I believe this to be a great book for self-study as well as for course use. The book is ideal for future probabilists as well as statisticians, and can serve as a good introduction for mathematicians interested in measure theory.’ Ita Cirovic Donev, MAA ReviewsReview of previous edition: ‘… succeeds in handling the technicalities of measure theory, which is traditionally regarded as dry and inaccessible to students (and, I think, the most difficult material that I have taught at undergraduate level) with a light touch. The book is eminently suitable for a course (or two) for good final-year or first-year post-graduate students and has the potential to revitalize the way that measure theory is taught.’ N. H. Bingham, Journal of the Royal Statistical SocietyReview of previous edition: ‘This book will remain a good reference on the subject for years to come.’ Peter Eichelsbacher, Mathematical ReviewsReview of previous edition: ‘… this well-written and carefully structured book is an excellent choice for an undergraduate course on measure and integration theory. Most good books on measure and integration are graduate books and, therefore, are not optimal for undergraduate courses … This book is aimed at both (future) analysts and (future) probabilists, and is therefore suitable for students from both these groups.’ Filip Lindskog, Journal of the American Statistical Association’This book is an admirable counterpart, both to the first author’s well-known text Measures, Integrals and Martingales (CUP, 2005/2017), and to the books on counter-examples in analysis (Gelbaum and Olmsted), topology (Steen and Seebach) and probability (Stoyanov). To paraphrase, the authors’ preface: in a good theory, it is valuable and instructive to probe the limits of what can be said by investigating what cannot be said. The task is thus well-conceived, and the execution is up to the standards one would expect from the books of the first author and of their papers. I recommend it warmly.’ Professor N. H. Bingham, Imperial College London Book Description A concise, elementary introduction to measure and integration theory, requiring few prerequisites as theory is developed quickly and simply. About the Author René L. Schilling is a Professor of Mathematics at Technische Universität, Dresden. His main research area is stochastic analysis and stochastic processes. Read more

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

⭐I have made it through over half the book and covering it carefully. It is excellent! I have read/skimmed several other measure theory books like Folland, Royden, Axler and this is my favorite. Wish I would have learned from this book first. It is gentle yet thorough in comparison to other texts.

⭐This is an excellent book, particularly for self-study. Clear and well-written, broad coverage, with appropriate exercises. The author has posted his solutions online. However, the Kindle version has many unreadable low-resolution bitmap-image equations; stick with the paper edition. 5 star book, minus 1 star for Kindle ebook issues.

⭐A little above my head at the moment, reading Bartle and Sherbert intro to real analysis before I dive in, but I think it will help me “immeasurably” (PUN) in my STAT grad courses on probability theory.

⭐Cover is easy to be broken. Other than that everything is great.

⭐The proofs of some of the theorems in the book are incomplete. The authors omits important logical steps (probably considers them obvious). And unless you are already familiar with the topic you often get stuck trying to understand how this sudden logical leap was done. I found that I had to look for some of the proofs elsewhere.The book reminds me more of lecture notes rather than a proper textbook.

⭐Very Nice book, i definitely recommend. This book perfect if one tries to self study.

⭐The book is excellent for use when taking a first course on Measures, Intergrals and Martingales. For instance, the chapter on Sigma-algebra explains very well what is a sigma-algebra on sets and what are the Borel sets. In fact I purchase that book because it has a full chapter on sigma-algebra. I did not find in any other textbooks a better explanation and presentation of sigma-algebra. Also, the author also provides on his web site solutions to the exercises at the end of each chapter.

⭐Il libro è ottimo per gli argomenti trattati e i molti esercizi tutti con soluzione disponibili. Le dimostrazioni sono svolte con molta chiarezza e rigore. Tutta via, alcuni punti sono trattati molto rapidamente.

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