Generalized Measure Theory

Author : Zhenyuan Wang,George J. Klir
Publisher : Springer Science & Business Media
Page : 392 pages
File Size : 44,9 Mb
Release : 2010-07-07
Category : Mathematics
ISBN : 9780387768526

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Generalized Measure Theory by Zhenyuan Wang,George J. Klir Pdf

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
Page : 790 pages
File Size : 54,8 Mb
Release : 2018-10-03
Category : Mathematics
ISBN : 9781482258103

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Measure Theory and Integration by M.M. Rao Pdf

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,George Klir
Publisher : Springer
Page : 0 pages
File Size : 55,9 Mb
Release : 2008-11-01
Category : Mathematics
ISBN : 0387568514

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Generalized Measure Theory by Wang Zhenyuan,George Klir Pdf

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 : Errett Bishop,Henry Cheng
Publisher : American Mathematical Soc.
Page : 85 pages
File Size : 41,8 Mb
Release : 1972
Category : Constructive mathematics
ISBN : 9780821818169

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Constructive Measure Theory by Errett Bishop,Henry Cheng Pdf

Author : Michael Eugene Taylor
Publisher : American Mathematical Soc.
Page : 346 pages
File Size : 48,6 Mb
Release : 2024-05-22
Category : Mathematics
ISBN : 082187246X

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Measure Theory and Integration by Michael Eugene Taylor Pdf

This self-contained treatment of measure and integration begins with a brief review of the Riemann integral and proceeds to a construction of Lebesgue measure on the real line. From there the reader is led to the general notion of measure, to the construction of the Lebesgue integral on a measure space, and to the major limit theorems, such as the Monotone and Dominated Convergence Theorems. The treatment proceeds to $Lp$ spaces, normed linear spaces that are shown to be complete (i.e., Banach spaces) due to the limit theorems. Particular attention is paid to $L2$ spaces as Hilbert spaces, with a useful geometrical structure. Having gotten quickly to the heart of the matter, the text proceeds to broaden its scope. There are further constructions of measures, including Lebesgue measure on $n$-dimensional Euclidean space. There are also discussions of surface measure, and more generally of Riemannian manifolds and the measures they inherit, and an appendix on the integration ofdifferential forms. Further geometric aspects are explored in a chapter on Hausdorff measure. The text also treats probabilistic concepts, in chapters on ergodic theory, probability spaces and random variables, Wiener measure and Brownian motion, and martingales. This text will prepare graduate students for more advanced studies in functional analysis, harmonic analysis, stochastic analysis, and geometric measure theory.

Author : J Yeh
Publisher : World Scientific Publishing Company
Page : 840 pages
File Size : 43,7 Mb
Release : 2014-06-11
Category : Mathematics
ISBN : 9789814578561

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Real Analysis by J Yeh Pdf

This book presents a unified treatise of the theory of measure and integration. In the setting of a general measure space, every concept is defined precisely and every theorem is presented with a clear and complete proof with all the relevant details. Counter-examples are provided to show that certain conditions in the hypothesis of a theorem cannot be simply dropped. The dependence of a theorem on earlier theorems is explicitly indicated in the proof, not only to facilitate reading but also to delineate the structure of the theory. The precision and clarity of presentation make the book an ideal textbook for a graduate course in real analysis while the wealth of topics treated also make the book a valuable reference work for mathematicians. The book is also very helpful to graduate students in statistics and electrical engineering, two disciplines that apply measure theory.

Author : Patrick Billingsley
Publisher : John Wiley & Sons
Page : 612 pages
File Size : 52,9 Mb
Release : 2017
Category : Electronic
ISBN : 8126517719

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Probability and Measure by Patrick Billingsley Pdf

Now in its new third edition, Probability and Measure offers advanced students, scientists, and engineers an integrated introduction to measure theory and probability. Retaining the unique approach of the previous editions, this text interweaves material on probability and measure, so that probability problems generate an interest in measure theory and measure theory is then developed and applied to probability. Probability and Measure provides thorough coverage of probability, measure, integration, random variables and expected values, convergence of distributions, derivatives and conditional probability, and stochastic processes. The Third Edition features an improved treatment of Brownian motion and the replacement of queuing theory with ergodic theory.· Probability· Measure· Integration· Random Variables and Expected Values· Convergence of Distributions· Derivatives and Conditional Probability· Stochastic Processes

Author : Donald L. Cohn
Publisher : Springer Science & Business Media
Page : 457 pages
File Size : 44,8 Mb
Release : 2013-07-13
Category : Mathematics
ISBN : 9781461469568

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Measure Theory by Donald L. Cohn Pdf

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.

Author : D. H. Fremlin
Publisher : Torres Fremlin
Page : 375 pages
File Size : 48,5 Mb
Release : 2000
Category : Fourier analysis
ISBN : 9780953812967

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Measure Theory by D. H. Fremlin Pdf

Author : Heinz Bauer
Publisher : Unknown
Page : 486 pages
File Size : 47,8 Mb
Release : 1981
Category : Mathematics
ISBN : UOM:39015042118292

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Probability Theory and Elements of Measure Theory by Heinz Bauer Pdf

Measure and integration theory; Probability theory; Continuation of measure and integration theory; Further development of probability theory.

Author : Ammar Khanfer
Publisher : Springer Nature
Page : 237 pages
File Size : 54,5 Mb
Release : 2023-09-08
Category : Mathematics
ISBN : 9789819928828

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Measure Theory and Integration by Ammar Khanfer Pdf

This textbook contains a detailed and thorough exposition of topics in measure theory and integration. With abundant solved examples and more than 200 problems, the book is written in a motivational and student-friendly manner. Targeted to senior undergraduate and graduate courses in mathematics, it provides a detailed and thorough explanation of all the concepts. Suitable for independent study, the book, the first of the three volumes, contains topics on measure theory, measurable functions, Lebesgue integration, Lebesgue spaces, and abstract measure theory.

Author : Richard Wheeden,Richard L. Wheeden,Antoni Zygmund
Publisher : CRC Press
Page : 289 pages
File Size : 55,6 Mb
Release : 1977-11-01
Category : Mathematics
ISBN : 9781482229530

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Measure and Integral by Richard Wheeden,Richard L. Wheeden,Antoni Zygmund Pdf

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 : Anonim
Publisher : Unknown
Page : 128 pages
File Size : 41,9 Mb
Release : 1977
Category : Electronic
ISBN : OCLC:233194384

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הפוסעים בדד by Anonim Pdf

Author : Rick Durrett
Publisher : Cambridge University Press
Page : 128 pages
File Size : 47,8 Mb
Release : 2010-08-30
Category : Mathematics
ISBN : 9781139491136

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Probability by Rick Durrett Pdf

This classic introduction to probability theory for beginning graduate students covers laws of large numbers, central limit theorems, random walks, martingales, Markov chains, ergodic theorems, and Brownian motion. It is a comprehensive treatment concentrating on the results that are the most useful for applications. Its philosophy is that the best way to learn probability is to see it in action, so there are 200 examples and 450 problems. The fourth edition begins with a short chapter on measure theory to orient readers new to the subject.

Author : Steven G. Krantz,Harold R. Parks
Publisher : Springer Science & Business Media
Page : 340 pages
File Size : 43,8 Mb
Release : 2008-12-15
Category : Mathematics
ISBN : 9780817646790

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Geometric Integration Theory by Steven G. Krantz,Harold R. Parks Pdf

This textbook introduces geometric measure theory through the notion of currents. Currents, continuous linear functionals on spaces of differential forms, are a natural language in which to formulate types of extremal problems arising in geometry, and can be used to study generalized versions of the Plateau problem and related questions in geometric analysis. Motivating key ideas with examples and figures, this book is a comprehensive introduction ideal for both self-study and for use in the classroom. The exposition demands minimal background, is self-contained and accessible, and thus is ideal for both graduate students and researchers.