Generalized Measure Theory
Title | Generalized Measure Theory PDF eBook |
Author | Zhenyuan Wang |
Publisher | Springer Science & Business Media |
Pages | 392 |
Release | 2010-07-07 |
Genre | Mathematics |
ISBN | 0387768521 |
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.
An Introduction to Measure Theory
Title | An Introduction to Measure Theory PDF eBook |
Author | Terence Tao |
Publisher | American Mathematical Soc. |
Pages | 206 |
Release | 2021-09-03 |
Genre | Education |
ISBN | 1470466406 |
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.
Generalized Measure Theory
Title | Generalized Measure Theory PDF eBook |
Author | Wang Zhenyuan |
Publisher | Springer |
Pages | 0 |
Release | 2008-11-01 |
Genre | Mathematics |
ISBN | 9780387568515 |
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.
Measure Theory and Integration
Title | Measure Theory and Integration PDF eBook |
Author | M.M. Rao |
Publisher | CRC Press |
Pages | 790 |
Release | 2018-10-03 |
Genre | Mathematics |
ISBN | 1482258102 |
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.
Generalized Measure Theory
Title | Generalized Measure Theory PDF eBook |
Author | Julia Eileen Grothaus Zerbe |
Publisher | |
Pages | 142 |
Release | 1979 |
Genre | |
ISBN |
Constructive Measure Theory
Title | Constructive Measure Theory PDF eBook |
Author | Errett Bishop |
Publisher | American Mathematical Soc. |
Pages | 95 |
Release | 1972 |
Genre | Constructive mathematics |
ISBN | 0821818163 |
Lectures on Geometric Measure Theory
Title | Lectures on Geometric Measure Theory PDF eBook |
Author | Leon Simon |
Publisher | |
Pages | 286 |
Release | 1984 |
Genre | Geometric measure theory |
ISBN | 9780867844290 |