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Physically beautiful and elegantly printed, organized and written lucidly, this volume is a welcome addition and an important contribution to mathematical literature. Therefore, Integration and Modern Analysis by Benedetto and Czaja had better have something special to distinguish itself Integration and Modern Analysis is not just your average cup of tea. Its goals go well beyond the usual prosaic objective of presenting rookie graduate students with a certain standard set of tools and skills in real analysis; Benedetto and Czaja aim to persuade the reader to their particular point of view and, indeed, to enlist him in their enterprise Well, Benedetto and Czaja have a wonderful product to sell and are right in doing such enthusiastic preaching of their cause.

If you incline in this direction of analysis, Integration and Modern Analysis is unquestionably your cup of tea. They find, that as yet in no textbook this point of view was carried through in an adequate way. Their text is intended as a remedy to the latter. As a consequence they include very carefully materials which are often omitted in monographs about real analysis and integration theory, such as Vitali's necessary and sufficient conditions for interchanging limits and integrals, the Vitali—Hahn—Saks theorem, but also, quite unusually, Grothendieck's theory of weak convergence of measures.

The presentation of the material becomes most vivid by numerous remarks concerning the historical genesis, by biographical notes on the most important contributors, especially about Vitali, by discussion of problems, and by an excellent choice of examples and comments for motivation to an extent, that seem to be unique This way a lot of information is provided and this makes the book interesting also for advanced study and for anybody interested in the field. The lively style of exposition makes the reading both instructive and agreeable. It can be recommended LV 4 , December, Convert currency.

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Evaluation Copy Request an Evaluation Copy. This is a dummy description. An in-depth look at real analysis and its applications-now expanded and revised. This new edition of the widely used analysis book continues to cover real analysis in greater detail and at a more advanced level than most books on the subject. Encompassing several subjects that underlie much of modern analysis, the book focuses on measure and integration theory, point set topology, and the basics of functional analysis.


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It illustrates the use of the general theories and introduces readers to other branches of analysis such as Fourier analysis, distribution theory, and probability theory. This edition is bolstered in content as well as in scope-extending its usefulness to students outside of pure analysis as well as those interested in dynamical systems. The numerous exercises, extensive bibliography, and review chapter on sets and metric spaces make Real Analysis: Modern Techniques and Their Applications, Second Edition invaluable for students in graduate-level analysis courses.

He has written extensively on mathematical analysis, including Fourier analysis, harmonic analysis, and differential equations. For additional information, see the Global Shipping Program terms and conditions - opens in a new window or tab This amount includes applicable customs duties, taxes, brokerage and other fees. For additional information, see the Global Shipping Program terms and conditions - opens in a new window or tab.

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Integration and modern analysis

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Oxford Mathematics 1st Year Student Lecture: Analysis III - Integration. Prof. Ben J. Green

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