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Author : William Howard Graves
Publisher :
ISBN 13 : 9781470401566
Total Pages : 72 pages
Book Rating : 4.4/5 (15 download)
Download or read book On the Theory of Vector Measures written by William Howard Graves and published by . This book was released on 1977 with total page 72 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Joseph Diestel
Publisher : American Mathematical Soc.
ISBN 13 : 0821815156
Total Pages : 322 pages
Book Rating : 4.8/5 (218 download)
Download or read book Vector Measures written by Joseph Diestel and published by American Mathematical Soc.. This book was released on 1977-06-01 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : William H. Graves
Publisher : Cambridge University Press
ISBN 13 : 9780821859537
Total Pages : 84 pages
Book Rating : 4.8/5 (595 download)
Download or read book On the theory of vector measures written by William H. Graves and published by Cambridge University Press. This book was released on 1977 with total page 84 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Klaus Bichteler
Publisher : Springer
ISBN 13 : 3540383697
Total Pages : 365 pages
Book Rating : 4.5/5 (43 download)
Download or read book Integration Theory written by Klaus Bichteler and published by Springer. This book was released on 2006-11-15 with total page 365 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Don H. Tucker
Publisher : Academic Press
ISBN 13 : 1483261026
Total Pages : 474 pages
Book Rating : 4.4/5 (832 download)
Download or read book Vector and Operator Valued Measures and Applications written by Don H. Tucker and published by Academic Press. This book was released on 2014-05-10 with total page 474 pages. Available in PDF, EPUB and Kindle. Book excerpt: Vector and Operator Valued Measures and Applications is a collection of papers presented at the Symposium on Vector and Operator Valued Measures and Applications held in Alta, Utah, on August 7-12, 1972. The symposium provided a forum for discussing vector and operator valued measures and their applications to various areas such as stochastic integration, electrical engineering, control theory, and scattering theory. Comprised of 37 chapters, this volume begins by presenting two remarks related to the result due to Kolmogorov: the first is a theorem holding for nonnegative definite functions from T X T to C (where T is an arbitrary index set), and the second applies to separable Hausdorff spaces T, continuous nonnegative definite functions ? from T X T to C, and separable Hilbert spaces H. The reader is then introduced to the extremal structure of the range of a controlled vector measure ? with values in a Hausdorff locally convex space X over the field of reals; how the theory of vector measures is connected with the theory of compact and weakly compact mappings on certain function spaces; and Daniell and Daniell-Bochner type integrals. Subsequent chapters focus on the disintegration of measures and lifting; products of spectral measures; and mean convergence of martingales of Pettis integrable functions. This book should be of considerable use to workers in the field of mathematics.
Author : Malempati Madhusudana Rao
Publisher : World Scientific
ISBN 13 : 9814350818
Total Pages : 553 pages
Book Rating : 4.8/5 (143 download)
Download or read book Random and Vector Measures written by Malempati Madhusudana Rao and published by World Scientific. This book was released on 2012 with total page 553 pages. Available in PDF, EPUB and Kindle. Book excerpt: Deals with the structural analysis of vector and random (or both) valued countably additive measures, and used for integral representations of random fields. This book analyzes several stationary aspects and related processes.
Author : Joe Diestel
Publisher : American Mathematical Society(RI)
ISBN 13 : 9781470412425
Total Pages : 338 pages
Book Rating : 4.4/5 (124 download)
Download or read book Vector Measures written by Joe Diestel and published by American Mathematical Society(RI). This book was released on 2014-06-06 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt: Examines the theory of measures having values in Banach spaces. This book deals with countably additive vector measures finitely additive vector measures, the Orlicz-Pettis theorem and its relatives. It also concentrates on measurable vector valued functions and the Bochner integral.
Author : Guillermo Curbera
Publisher : Springer Science & Business Media
ISBN 13 : 3034602111
Total Pages : 382 pages
Book Rating : 4.0/5 (346 download)
Download or read book Vector Measures, Integration and Related Topics written by Guillermo Curbera and published by Springer Science & Business Media. This book was released on 2010-02-21 with total page 382 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : N. Dinculeanu
Publisher : Elsevier
ISBN 13 : 1483222659
Total Pages : 446 pages
Book Rating : 4.4/5 (832 download)
Download or read book Vector Measures written by N. Dinculeanu and published by Elsevier. This book was released on 2014-07-21 with total page 446 pages. Available in PDF, EPUB and Kindle. Book excerpt: International Series of Monographs in Pure and Applied Mathematics, Volume 95: Vector Measures focuses on the study of measures with values in a Banach space, including positive measures with finite or infinite values. This book is organized into three chapters. Chapter I covers classes of sets, set functions, variation and semi-variation of set functions, and extension of set functions from a certain class to a wider one. The integration of vector functions with respect to vector measures is reviewed in Chapter II. In Chapter III, the regular measures on a locally compact space and integral representation of the dominated operations on the space of continuous functions with compact carrier are described. This volume is intended for specialists, researchers, and students interested in vector measures.
Author : V. M. Bogdan
Publisher :
ISBN 13 :
Total Pages : 78 pages
Book Rating : 4.F/5 ( download)
Download or read book Topological Rings of Sets and the Theory of Vector Measures written by V. M. Bogdan and published by . This book was released on 1978 with total page 78 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Terence Tao
Publisher : American Mathematical Soc.
ISBN 13 : 1470466406
Total Pages : 206 pages
Book Rating : 4.4/5 (74 download)
Download or read book An Introduction to Measure Theory written by Terence Tao and published by American Mathematical Soc.. This book was released on 2021-09-03 with total page 206 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : N. U. Ahmed
Publisher : Springer Nature
ISBN 13 : 3030821390
Total Pages : 328 pages
Book Rating : 4.0/5 (38 download)
Download or read book Optimal Control of Dynamic Systems Driven by Vector Measures written by N. U. Ahmed and published by Springer Nature. This book was released on 2021-09-13 with total page 328 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to the development of optimal control theory for finite dimensional systems governed by deterministic and stochastic differential equations driven by vector measures. The book deals with a broad class of controls, including regular controls (vector-valued measurable functions), relaxed controls (measure-valued functions) and controls determined by vector measures, where both fully and partially observed control problems are considered. In the past few decades, there have been remarkable advances in the field of systems and control theory thanks to the unprecedented interaction between mathematics and the physical and engineering sciences. Recently, optimal control theory for dynamic systems driven by vector measures has attracted increasing interest. This book presents this theory for dynamic systems governed by both ordinary and stochastic differential equations, including extensive results on the existence of optimal controls and necessary conditions for optimality. Computational algorithms are developed based on the optimality conditions, with numerical results presented to demonstrate the applicability of the theoretical results developed in the book. This book will be of interest to researchers in optimal control or applied functional analysis interested in applications of vector measures to control theory, stochastic systems driven by vector measures, and related topics. In particular, this self-contained account can be a starting point for further advances in the theory and applications of dynamic systems driven and controlled by vector measures.
Author : M.M. Rao
Publisher : CRC Press
ISBN 13 : 1482258102
Total Pages : 790 pages
Book Rating : 4.4/5 (822 download)
Download or read book Measure Theory and Integration written by M.M. Rao and published by CRC Press. This book was released on 2018-10-03 with total page 790 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Donald L. Cohn
Publisher : Springer Science & Business Media
ISBN 13 : 1489903992
Total Pages : 379 pages
Book Rating : 4.4/5 (899 download)
Download or read book Measure Theory written by Donald L. Cohn and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 379 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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. Measure Theory provides a solid background for study in both harmonic analysis and probability theory and is an excellent resource for advanced undergraduate and graduate students in mathematics. The prerequisites for this book are courses in topology and analysis.
Author : Robert B. Ash
Publisher : Academic Press
ISBN 13 : 1483265102
Total Pages : 300 pages
Book Rating : 4.4/5 (832 download)
Download or read book Measure, Integration, and Functional Analysis written by Robert B. Ash and published by Academic Press. This book was released on 2014-05-10 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt: Measure, Integration, and Functional Analysis deals with the mathematical concepts of measure, integration, and functional analysis. The fundamentals of measure and integration theory are discussed, along with the interplay between measure theory and topology. Comprised of four chapters, this book begins with an overview of the basic concepts of the theory of measure and integration as a prelude to the study of probability, harmonic analysis, linear space theory, and other areas of mathematics. The reader is then introduced to a variety of applications of the basic integration theory developed in the previous chapter, with particular reference to the Radon-Nikodym theorem. The third chapter is devoted to functional analysis, with emphasis on various structures that can be defined on vector spaces. The final chapter considers the connection between measure theory and topology and looks at a result that is a companion to the monotone class theorem, together with the Daniell integral and measures on topological spaces. The book concludes with an assessment of measures on uncountably infinite product spaces and the weak convergence of measures. This book is intended for mathematics majors, most likely seniors or beginning graduate students, and students of engineering and physics who use measure theory or functional analysis in their work.
Author : C. Constantinescu
Publisher : Springer
ISBN 13 : 3540392750
Total Pages : 202 pages
Book Rating : 4.5/5 (43 download)
Download or read book Duality in Measure Theory written by C. Constantinescu and published by Springer. This book was released on 2006-11-15 with total page 202 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : D. Kölzow
Publisher : Springer
ISBN 13 : 3540392211
Total Pages : 592 pages
Book Rating : 4.5/5 (43 download)
Download or read book Measure Theory Oberwolfach 1979 written by D. Kölzow and published by Springer. This book was released on 2006-11-15 with total page 592 pages. Available in PDF, EPUB and Kindle. Book excerpt:
