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Author: Joseph Diestel
Publisher: American Mathematical Soc.
ISBN: 0821815156
Category : Mathematics
Languages : en
Pages : 338
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Book Description
In this survey the authors endeavor to give a comprehensive examination of the theory of measures having values in Banach spaces. The interplay between topological and geometric properties of Banach spaces and the properties of measures having values in Banach spaces is the unifying theme. The first chapter deals with countably additive vector measures finitely additive vector measures, the Orlicz-Pettis theorem and its relatives. Chapter II concentrates on measurable vector valued functions and the Bochner integral. Chapter III begins the study of the interplay among the Radon-Nikodym theorem for vector measures, operators on $L_1$ and topological properties of Banach spaces. A variety of applications is given in the next chapter. Chapter V deals with martingales of Bochner integrable functions and their relation to dentable subsets of Banach spaces. Chapter VI is devoted to a measure-theoretic study of weakly compact absolutely summing and nuclear operators on spaces of continuous functions. In Chapter VII a detailed study of the geometry of Banach spaces with the Radon-Nikodym property is given. The next chapter deals with the use of Radon-Nikodym theorems in the study of tensor products of Banach spaces. The last chapter concludes the survey with a discussion of the Liapounoff convexity theorem and other geometric properties of the range of a vector measure. Accompanying each chapter is an extensive survey of the literature and open problems.
Author: Walter Roth
Publisher: Springer Science & Business Media
ISBN: 3540875646
Category : Mathematics
Languages : en
Pages : 370
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Book Description
Integration theory deals with extended real-valued, vector-valued, or operator-valued measures and functions, but different approaches are used for each case. This book develops a general theory of integration that simultaneously deals with all three cases.
Author: Joseph Diestel
Publisher: American Mathematical Soc.
ISBN: 0821815156
Category : Mathematics
Languages : en
Pages : 338
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Book Description
In this survey the authors endeavor to give a comprehensive examination of the theory of measures having values in Banach spaces. The interplay between topological and geometric properties of Banach spaces and the properties of measures having values in Banach spaces is the unifying theme. The first chapter deals with countably additive vector measures finitely additive vector measures, the Orlicz-Pettis theorem and its relatives. Chapter II concentrates on measurable vector valued functions and the Bochner integral. Chapter III begins the study of the interplay among the Radon-Nikodym theorem for vector measures, operators on $L_1$ and topological properties of Banach spaces. A variety of applications is given in the next chapter. Chapter V deals with martingales of Bochner integrable functions and their relation to dentable subsets of Banach spaces. Chapter VI is devoted to a measure-theoretic study of weakly compact absolutely summing and nuclear operators on spaces of continuous functions. In Chapter VII a detailed study of the geometry of Banach spaces with the Radon-Nikodym property is given. The next chapter deals with the use of Radon-Nikodym theorems in the study of tensor products of Banach spaces. The last chapter concludes the survey with a discussion of the Liapounoff convexity theorem and other geometric properties of the range of a vector measure. Accompanying each chapter is an extensive survey of the literature and open problems.
Author: Thiruvaiyaru V. Panchapagesan
Publisher: Springer Science & Business Media
ISBN: 3764386029
Category : Mathematics
Languages : en
Pages : 311
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Book Description
This volume is a thorough and comprehensive treatise on vector measures, treating the vectorial Radon integration in detail. It explores an interplay between, on the one side, linear operators, transferring real (complex) functions onto elements of locally convex Hausdorff spaces, and vector-valued measures, on the other. The book contains not only a large amount of new material but also corrects various errors in well-known results available in the literature.
Author: Guillermo Curbera
Publisher: Springer Science & Business Media
ISBN: 3034602111
Category : Mathematics
Languages : en
Pages : 382
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Book Description
This volume contains a selection of articles on the theme "vector measures, integration and applications" together with some related topics. The articles consist of both survey style and original research papers, are written by experts in thearea and present a succinct account of recent and up-to-date knowledge. The topic is interdisciplinary by nature and involves areas such as measure and integration (scalar, vector and operator-valued), classical and harmonic analysis, operator theory, non-commutative integration, andfunctional analysis. The material is of interest to experts, young researchers and postgraduate students.
Author: Don H. Tucker
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 488
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Book Description
Author: Michel Métivier
Publisher: Walter de Gruyter
ISBN: 3110845563
Category : Mathematics
Languages : en
Pages : 305
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Book Description
The series is devoted to the publication of monographs and high-level textbooks in mathematics, mathematical methods and their applications. Apart from covering important areas of current interest, a major aim is to make topics of an interdisciplinary nature accessible to the non-specialist. The works in this series are addressed to advanced students and researchers in mathematics and theoretical physics. In addition, it can serve as a guide for lectures and seminars on a graduate level. The series de Gruyter Studies in Mathematics was founded ca. 30 years ago by the late Professor Heinz Bauer and Professor Peter Gabriel with the aim to establish a series of monographs and textbooks of high standard, written by scholars with an international reputation presenting current fields of research in pure and applied mathematics. While the editorial board of the Studies has changed with the years, the aspirations of the Studies are unchanged. In times of rapid growth of mathematical knowledge carefully written monographs and textbooks written by experts are needed more than ever, not least to pave the way for the next generation of mathematicians. In this sense the editorial board and the publisher of the Studies are devoted to continue the Studies as a service to the mathematical community. Please submit any book proposals to Niels Jacob.
Author: E. Pap
Publisher: Elsevier
ISBN: 0080533094
Category : Mathematics
Languages : en
Pages : 1633
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Book Description
The main goal of this Handbook isto survey measure theory with its many different branches and itsrelations 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 whichsupport the idea of "measure" in a wider sense, e.g. the ninth part of the Handbook. Although chapters are written of surveys in the variousareas they contain many special topics and challengingproblems valuable for experts and rich sources of inspiration.Mathematicians from other areas as well as physicists, computerscientists, engineers and econometrists will find useful results andpowerful methods for their research. The reader may find in theHandbook many close relations to other mathematical areas: realanalysis, probability theory, statistics, ergodic theory,functional analysis, potential theory, topology, set theory,geometry, differential equations, optimization, variationalanalysis, decision making and others. The Handbook is a richsource of relevant references to articles, books and lecturenotes and it contains for the reader's convenience an extensivesubject and author index.
Author: M.M. Rao
Publisher: CRC Press
ISBN: 1351991485
Category : Mathematics
Languages : en
Pages : 794
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Book 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.
Author: A. Bellow
Publisher: Springer
ISBN: 3540381074
Category : Mathematics
Languages : en
Pages : 423
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Book Description
Author: Honglei Xu
Publisher: Springer
ISBN: 3662434040
Category : Mathematics
Languages : en
Pages : 268
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Book Description
This book presents advances in state-of-the-art solution methods and their applications to real life practical problems in optimization, control and operations research. Contributions from world-class experts in the field are collated here in two parts, dealing first with optimization and control theory and then with techniques and applications. Topics covered in the first part include control theory on infinite dimensional Banach spaces, history-dependent inclusion and linear programming complexity theory. Chapters also explore the use of approximations of Hamilton-Jacobi-Bellman inequality for solving periodic optimization problems and look at multi-objective semi-infinite optimization problems and production planning problems. In the second part, the authors address techniques and applications of optimization and control in a variety of disciplines, such as chaos synchronization, facial expression recognition and dynamic input-output economic models. Other applications considered here include image retrieval, natural earth satellites orbital transfers, snap-back repellers and modern logistic systems. Readers will learn of advances in optimization, control and operations research, as well as potential new avenues of research and development. The book will appeal to scientific researchers, mathematicians and all specialists interested in the latest advances in optimization and control.
