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.
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10 of 10 people found the following review helpful:
5.0 out of 5 stars
A gemstone for students,
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This review is from: Real Analysis: Theory of Measure and Integration (Hardcover)
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.
5 of 5 people found the following review helpful:
5.0 out of 5 stars
Good book for non-analysts,
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This review is from: Real Analysis: Theory of Measure And Integration (Paperback)
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.
5.0 out of 5 stars
The only book on measure theory you'll need,
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This review is from: Real Analysis: Theory of Measure And Integration (Paperback)
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.)
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Key Phrases - Statistically Improbable Phrases (SIPs):
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signed measure space, shrinks nicely, consider the product measure space, regular outer measure, disjoint finite sequence, identically vanishing function, complete measure space, finite disjoint subcollection, arbitrary measure space, shrink nicely, nonnegative simple functions, metric outer measure, two normed linear spaces, finite subadditivity, countably additive set function, finite disjoint collection, disjoint sequence, countable subadditivity, many real values, countable disjoint collection, spherical hypersurface, outer regularity, covering sequence, finite open interval, essential bound Key Phrases - Capitalized Phrases (CAPs): (learn more)
The Classical Banach Spaces, Problems Prob, Proof of Theorem, Hölder's Inequality, Bounded Convergence Theorem, Intermediate Value Theorem, Mean Value Theorem, Riesz Representation Theorem, Vitali Covering Theorem, Applying Proposition, Egoroff's Theorem, Hausdorff Measures, Urysohn's Lemma, Baire Category Theorem, Borel-Cantelli Lemma, Combining Theorem, Jensen's Inequality, Measure Definition, Proof of Proposition, Extension of Additive Set Functions, Hopf Extension Theorem, Proof of Lemma, Schwarz's Inequality, Suppose the Radon-Nikodym, Zorn's Lemma New!
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Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
signed measure space, shrinks nicely, consider the product measure space, regular outer measure, disjoint finite sequence, identically vanishing function, complete measure space, finite disjoint subcollection, arbitrary measure space, shrink nicely, nonnegative simple functions, metric outer measure, two normed linear spaces, finite subadditivity, countably additive set function, finite disjoint collection, disjoint sequence, countable subadditivity, many real values, countable disjoint collection, spherical hypersurface, outer regularity, covering sequence, finite open interval, essential bound Key Phrases - Capitalized Phrases (CAPs): (learn more)
The Classical Banach Spaces, Problems Prob, Proof of Theorem, Hölder's Inequality, Bounded Convergence Theorem, Intermediate Value Theorem, Mean Value Theorem, Riesz Representation Theorem, Vitali Covering Theorem, Applying Proposition, Egoroff's Theorem, Hausdorff Measures, Urysohn's Lemma, Baire Category Theorem, Borel-Cantelli Lemma, Combining Theorem, Jensen's Inequality, Measure Definition, Proof of Proposition, Extension of Additive Set Functions, Hopf Extension Theorem, Proof of Lemma, Schwarz's Inequality, Suppose the Radon-Nikodym, Zorn's Lemma New!
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Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 14
books:
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- Advanced Calculus by R. Creighton Buck in Front Matter, and Back Matter
- Real Analysis by Andrew M. Bruckner in Back Matter
- Mathematical Analysis by Wiley in Back Matter
- Measure Theory (Graduate Texts in Mathematics) (v. 18) by Paul R. Halmos in Back Matter
- Probability and Measure, 3rd Edition by Patrick Billingsley in Back Matter
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