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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[,] offering valuable examples, exercises, and applications. This book examines the Henstock-Kurzweil integral with approaches not found in any other text.
- L'Enseignement Mathematique, Vol. 50, 1-2, Jan-Jun 2004
This monograph provides a significantly revised and expanded version of the original edition published in 1987 on the classical topics in measure theory and integration. …The book is well understandable and requires only a basic knowledge of advanced calculus….It can be warmly recommended to a broad spectrum of reader - to graduate students as well as young researchers who wish to become acquainted with the basic elements and deeper properties of abstract analysis and its applications.
-EMS Newsletter, March 2006
- L'Enseignement Mathematique, Vol. 50, 1-2, Jan-Jun 2004
This monograph provides a significantly revised and expanded version of the original edition published in 1987 on the classical topics in measure theory and integration. …The book is well understandable and requires only a basic knowledge of advanced calculus….It can be warmly recommended to a broad spectrum of reader - to graduate students as well as young researchers who wish to become acquainted with the basic elements and deeper properties of abstract analysis and its applications.
-EMS Newsletter, March 2006
Product Description
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.
With more than 170 references for further investigation of the subject, this Second Edition
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.
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Inside This Book
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First Sentence:
After a discussion of the need for a general study of measures and integration, an overview of the subject is sketched. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
finite subset property, nonabsolute integration, generated outer measure, strict localizability, nonabsolute integrals, finite measurable functions, complete measure space, metric outer measure, nonmeasurable functions, regular outer measure, strong additivity, outer capacity, real measurable functions, abstract measure space, lifting map, linear metric space, inner regularity, linear lifting, outer regularity, finite measure space, arbitrary measure space, taking infima, measurable group, adjoint space, lifting theorem Key Phrases - Capitalized Phrases (CAPs): (learn more)
Classical Integration, Exercises Let, Extend Proposition, Sketch of Proof New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
After a discussion of the need for a general study of measures and integration, an overview of the subject is sketched. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
finite subset property, nonabsolute integration, generated outer measure, strict localizability, nonabsolute integrals, finite measurable functions, complete measure space, metric outer measure, nonmeasurable functions, regular outer measure, strong additivity, outer capacity, real measurable functions, abstract measure space, lifting map, linear metric space, inner regularity, linear lifting, outer regularity, finite measure space, arbitrary measure space, taking infima, measurable group, adjoint space, lifting theorem Key Phrases - Capitalized Phrases (CAPs): (learn more)
Classical Integration, Exercises Let, Extend Proposition, Sketch of Proof New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 89
books:
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34
books
cite this book:
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- Set Theory by Thomas Jech in Front Matter (1), Front Matter (2), and Front Matter (3)
- Introduction to Set Theory, Third Edition, Revised and Expanded (Pure and Applied Mathematics) by Karel Hrbacek in Front Matter (1), Front Matter (2), and Front Matter (3)
- The General Theory of Integration (Oxford Mathematical Monographs) by Ralph Henstock in Back Matter (1), and Back Matter (2)
- Fundamentals of Pattern Recognition (Pure and Applied Mathematics) by Monique L. Pavel in Front Matter (1), and Front Matter (2)
- Geometric Measure Theory (Classics in Mathematics) by Herbert Federer in Front Matter, and Back Matter
See all 89 books this book cites
- Stochastic Processes and Functional Analysis (Lecture Notes in Pure and Applied Mathematics) by Jerome Goldstein in Front Matter, and page 197
- Stochastic Processes and Functional Analysis: A Volume of Recent Advances in Honor of M. M. Rao (Lecture Notes in Pure and Applied Mathematics) by Alan C. Krinik in Front Matter, and page 7
- A Guide to the Literature on Semirings and their Applications in Mathematics and Information Sciences: With Complete Bibliography by K. Glazek in Front Matter, and Back Matter
- Hopf Algebras in Noncommutative Geometry and Physics (Lecture Notes in Pure and Applied Mathematics) by Stefaan Caenepeel in Front Matter (1), and Front Matter (2)
- Optimized Bayesian Dynamic Advising: Theory and Algorithms (Advanced Information and Knowledge Processing) by Miroslav Karny in Back Matter
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