Generalized Measure Theory

Author : Zhenyuan Wang
Publisher : Springer Science & Business Media
ISBN 13 : 0387768521
Total Pages : 392 pages
Book Rating : 4.26/5 ( download)

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Download or read book Generalized Measure Theory written by Zhenyuan Wang and published by Springer Science & Business Media. This book was released on 2010-07-07 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: Generalized Measure Theory examines the relatively new mathematical area of generalized measure theory. The exposition unfolds systematically, beginning with preliminaries and new concepts, followed by a detailed treatment of important new results regarding various types of nonadditive measures and the associated integration theory. The latter involves several types of integrals: Sugeno integrals, Choquet integrals, pan-integrals, and lower and upper integrals. All of the topics are motivated by numerous examples, culminating in a final chapter on applications of generalized measure theory. Some key features of the book include: many exercises at the end of each chapter along with relevant historical and bibliographical notes, an extensive bibliography, and name and subject indices. The work is suitable for a classroom setting at the graduate level in courses or seminars in applied mathematics, computer science, engineering, and some areas of science. A sound background in mathematical analysis is required. Since the book contains many original results by the authors, it will also appeal to researchers working in the emerging area of generalized measure theory.

Author : M.M. Rao
Publisher : CRC Press
ISBN 13 : 1482258102
Total Pages : 790 pages
Book Rating : 4.03/5 ( download)

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Download or read book Measure Theory and Integration written by M.M. Rao and published by CRC Press. This book was released on 2018-10-03 with total page 790 pages. Available in PDF, EPUB and Kindle. Book excerpt: Significantly revised and expanded, this authoritative reference/text comprehensively describes concepts in measure theory, classical integration, and generalized Riemann integration of both scalar and vector types-providing a complete and detailed review of every aspect of measure and integration theory using valuable examples, exercises, and applications. With more than 170 references for further investigation of the subject, this Second Edition provides more than 60 pages of new information, as well as a new chapter on nonabsolute integrals contains extended discussions on the four basic results of Banach spaces presents an in-depth analysis of the classical integrations with many applications, including integration of nonmeasurable functions, Lebesgue spaces, and their properties details the basic properties and extensions of the Lebesgue-Carathéodory measure theory, as well as the structure and convergence of real measurable functions covers the Stone isomorphism theorem, the lifting theorem, the Daniell method of integration, and capacity theory Measure Theory and Integration, Second Edition is a valuable reference for all pure and applied mathematicians, statisticians, and mathematical analysts, and an outstanding text for all graduate students in these disciplines.

Author : Wang Zhenyuan
Publisher : Springer
ISBN 13 : 9780387568515
Total Pages : 0 pages
Book Rating : 4.14/5 ( download)

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Download or read book Generalized Measure Theory written by Wang Zhenyuan and published by Springer. This book was released on 2008-11-01 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Generalized Measure Theory examines the relatively new mathematical area of generalized measure theory. The exposition unfolds systematically, beginning with preliminaries and new concepts, followed by a detailed treatment of important new results regarding various types of nonadditive measures and the associated integration theory. The latter involves several types of integrals: Sugeno integrals, Choquet integrals, pan-integrals, and lower and upper integrals. All of the topics are motivated by numerous examples, culminating in a final chapter on applications of generalized measure theory. Some key features of the book include: many exercises at the end of each chapter along with relevant historical and bibliographical notes, an extensive bibliography, and name and subject indices. The work is suitable for a classroom setting at the graduate level in courses or seminars in applied mathematics, computer science, engineering, and some areas of science. A sound background in mathematical analysis is required. Since the book contains many original results by the authors, it will also appeal to researchers working in the emerging area of generalized measure theory.

Author : Terence Tao
Publisher : American Mathematical Soc.
ISBN 13 : 1470466406
Total Pages : 206 pages
Book Rating : 4.04/5 ( download)

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Download or read book An Introduction to Measure Theory written by Terence Tao and published by American Mathematical Soc.. This book was released on 2021-09-03 with total page 206 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a graduate text introducing the fundamentals of measure theory and integration theory, which is the foundation of modern real analysis. The text focuses first on the concrete setting of Lebesgue measure and the Lebesgue integral (which in turn is motivated by the more classical concepts of Jordan measure and the Riemann integral), before moving on to abstract measure and integration theory, including the standard convergence theorems, Fubini's theorem, and the Carathéodory extension theorem. Classical differentiation theorems, such as the Lebesgue and Rademacher differentiation theorems, are also covered, as are connections with probability theory. The material is intended to cover a quarter or semester's worth of material for a first graduate course in real analysis. There is an emphasis in the text on tying together the abstract and the concrete sides of the subject, using the latter to illustrate and motivate the former. The central role of key principles (such as Littlewood's three principles) as providing guiding intuition to the subject is also emphasized. There are a large number of exercises throughout that develop key aspects of the theory, and are thus an integral component of the text. As a supplementary section, a discussion of general problem-solving strategies in analysis is also given. The last three sections discuss optional topics related to the main matter of the book.

Author : Julia Eileen Grothaus Zerbe
Publisher :
ISBN 13 :
Total Pages : 142 pages
Book Rating : 4.26/5 ( download)

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Download or read book Generalized Measure Theory written by Julia Eileen Grothaus Zerbe and published by . This book was released on 1979 with total page 142 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Errett Bishop
Publisher : American Mathematical Soc.
ISBN 13 : 0821818163
Total Pages : 95 pages
Book Rating : 4.69/5 ( download)

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Download or read book Constructive Measure Theory written by Errett Bishop and published by American Mathematical Soc.. This book was released on 1972 with total page 95 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Richard Wheeden
Publisher : CRC Press
ISBN 13 : 1482229536
Total Pages : 289 pages
Book Rating : 4.30/5 ( download)

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Download or read book Measure and Integral written by Richard Wheeden and published by CRC Press. This book was released on 1977-11-01 with total page 289 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume develops the classical theory of the Lebesgue integral and some of its applications. The integral is initially presented in the context of n-dimensional Euclidean space, following a thorough study of the concepts of outer measure and measure. A more general treatment of the integral, based on an axiomatic approach, is later given.

Author : Leon Simon
Publisher :
ISBN 13 : 9780867844290
Total Pages : 286 pages
Book Rating : 4.99/5 ( download)

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Download or read book Lectures on Geometric Measure Theory written by Leon Simon and published by . This book was released on 1984 with total page 286 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Vladimir I. Bogachev
Publisher : Springer Science & Business Media
ISBN 13 : 3540345140
Total Pages : 1075 pages
Book Rating : 4.45/5 ( download)

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Download or read book Measure Theory written by Vladimir I. Bogachev and published by Springer Science & Business Media. This book was released on 2007-01-15 with total page 1075 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book giving an exposition of the foundations of modern measure theory offers three levels of presentation: a standard university graduate course, an advanced study containing some complements to the basic course, and, finally, more specialized topics partly covered by more than 850 exercises with detailed hints and references. Bibliographical comments and an extensive bibliography with 2000 works covering more than a century are provided.

Author : Donald L. Cohn
Publisher : Springer Science & Business Media
ISBN 13 : 1461469562
Total Pages : 466 pages
Book Rating : 4.68/5 ( download)

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Download or read book Measure Theory written by Donald L. Cohn and published by Springer Science & Business Media. This book was released on 2013-07-13 with total page 466 pages. Available in PDF, EPUB and Kindle. Book excerpt: Intended as a self-contained introduction to measure theory, this textbook also includes a comprehensive treatment of integration on locally compact Hausdorff spaces, the analytic and Borel subsets of Polish spaces, and Haar measures on locally compact groups. This second edition includes a chapter on measure-theoretic probability theory, plus brief treatments of the Banach-Tarski paradox, the Henstock-Kurzweil integral, the Daniell integral, and the existence of liftings. Measure Theory provides a solid background for study in both functional analysis and probability theory and is an excellent resource for advanced undergraduate and graduate students in mathematics. The prerequisites for this book are basic courses in point-set topology and in analysis, and the appendices present a thorough review of essential background material.