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Author | : Zhenyuan Wang |
Publisher | : Springer Science & Business Media |
Total Pages | : 392 |
Release | : 2010-07-07 |
Genre | : Mathematics |
ISBN | : 0387768521 |
Download Generalized Measure Theory Book in PDF, ePub and Kindle
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 | : Wang Zhenyuan |
Publisher | : Springer |
Total Pages | : 0 |
Release | : 2008-11-01 |
Genre | : Mathematics |
ISBN | : 9780387568515 |
Download Generalized Measure Theory Book in PDF, ePub and Kindle
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. |
Total Pages | : 206 |
Release | : 2021-09-03 |
Genre | : Education |
ISBN | : 1470466406 |
Download An Introduction to Measure Theory Book in PDF, ePub and Kindle
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 | : M.M. Rao |
Publisher | : CRC Press |
Total Pages | : 790 |
Release | : 2018-10-03 |
Genre | : Mathematics |
ISBN | : 1482258102 |
Download Measure Theory and Integration Book in PDF, ePub and Kindle
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 | : Richard Wheeden |
Publisher | : CRC Press |
Total Pages | : 289 |
Release | : 1977-11-01 |
Genre | : Mathematics |
ISBN | : 1482229536 |
Download Measure and Integral Book in PDF, ePub and Kindle
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 | : Errett Bishop |
Publisher | : American Mathematical Soc. |
Total Pages | : 95 |
Release | : 1972 |
Genre | : Constructive mathematics |
ISBN | : 0821818163 |
Download Constructive Measure Theory Book in PDF, ePub and Kindle
Author | : Vladimir I. Bogachev |
Publisher | : Springer Science & Business Media |
Total Pages | : 1075 |
Release | : 2007-01-15 |
Genre | : Mathematics |
ISBN | : 3540345140 |
Download Measure Theory Book in PDF, ePub and Kindle
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 | : E. Pap |
Publisher | : Elsevier |
Total Pages | : 1632 |
Release | : 2002-10-31 |
Genre | : Mathematics |
ISBN | : 9780080533094 |
Download Handbook of Measure Theory Book in PDF, ePub and Kindle
The main goal of this Handbook is to survey measure theory with its many different branches and its relations with other areas of mathematics. Mostly aggregating many classical branches of measure theory the aim of the Handbook is also to cover new fields, approaches and applications which support the idea of "measure" in a wider sense, e.g. the ninth part of the Handbook. Although chapters are written of surveys in the various areas they contain many special topics and challenging problems valuable for experts and rich sources of inspiration. Mathematicians from other areas as well as physicists, computer scientists, engineers and econometrists will find useful results and powerful methods for their research. The reader may find in the Handbook many close relations to other mathematical areas: real analysis, probability theory, statistics, ergodic theory, functional analysis, potential theory, topology, set theory, geometry, differential equations, optimization, variational analysis, decision making and others. The Handbook is a rich source of relevant references to articles, books and lecture notes and it contains for the reader's convenience an extensive subject and author index.
Author | : Leon Simon |
Publisher | : |
Total Pages | : 286 |
Release | : 1984 |
Genre | : Geometric measure theory |
ISBN | : 9780867844290 |
Download Lectures on Geometric Measure Theory Book in PDF, ePub and Kindle
Author | : V.S. Vladimirov |
Publisher | : Springer Science & Business Media |
Total Pages | : 308 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 9400928319 |
Download Tauberian Theorems for Generalized Functions Book in PDF, ePub and Kindle
Approach your problems from the right end It isn't that they can't see the solution. It is and begin with the answers. Then one day, that they can't see the problem. perhaps you will find the final question. The Scandal of Father G. K. Chesterton. 'The Hermit Clad in Crane Feathers' in R. Brown 'The point of a Pin'. van Gulik's The Chinese Maze Murders. Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non trivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces. And in addition to this there are such new emerging subdisciplines as "experimental mathematics", "CFD", "completely integrable systems", "chaos, synergetics and large-scale order", which are almost impossible to fit into the existing classification schemes. They draw upon widely different sections of mathematics.