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Vector Measures
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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.
Book Synopsis Vector Measures, Integration and Related Topics by : Guillermo Curbera
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.
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.
Book Synopsis Random and Vector Measures by : Malempati Madhusudana Rao
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.
Book Synopsis Vector Measures and Control Systems by :
Download or read book Vector Measures and Control Systems written by and published by Elsevier. This book was released on 2011-09-21 with total page 179 pages. Available in PDF, EPUB and Kindle. Book excerpt: Vector Measures and Control Systems
Book Synopsis BanachâHilbert Spaces, Vector Measures and Group Representations by : TsoyâWo Ma
Download or read book BanachâHilbert Spaces, Vector Measures and Group Representations written by TsoyâWo Ma and published by World Scientific Publishing Company. This book was released on 2002-06-13 with total page 620 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an elementary introduction to classical analysis on normed spaces, with special attention paid to fixed points, calculus, and ordinary differential equations. It contains a full treatment of vector measures on delta rings without assuming any scalar measure theory and hence should fit well into existing courses. The relation between group representations and almost periodic functions is presented. The mean values offer an infinitedimensional analogue of measure theory on finitedimensional Euclidean spaces. This book is ideal for beginners who want to get through the basic material as soon as possible and then do their own research immediately.
Book Synopsis On the Theory of Vector Measures by : William Howard Graves
Download or read book On the Theory of Vector Measures written by William Howard Graves and published by American Mathematical Soc.. This book was released on 1977 with total page 72 pages. Available in PDF, EPUB and Kindle. Book excerpt: Given a ring of subsets of a non-empty set, there is a universal measure on the ring with values in an associated complete locally convex space which carries, through its typology, much of the combinatorial and measure theoretic structure of the ring. Moreover, vector measures of the ring are in 1-1 correspondence with continuous linear maps on the associated space. Several aspects of the theory of vector measures including decomposition theorems, extension theorems, Bartle-Dunford-Schwartz type theorems on weak compactness, and Pettis and Orlicz-Pettis-type theorems are studied in the unifying context of the universal measure and the associated universal representation theorem. A brief account of a similar theory for measures on abstract Boolean algebras is also given.
Book Synopsis Optimal Control of Dynamic Systems Driven by Vector Measures by : N. U. Ahmed
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.
Book Synopsis Vector and Operator Valued Measures and Applications by : Don H. Tucker
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.
Book Synopsis Optimal Control of Dynamic Systems Driven by Vector Measures by : N. U. Ahmed
Download or read book Optimal Control of Dynamic Systems Driven by Vector Measures written by N. U. Ahmed and published by . This book was released on 2021 with total page 0 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.
Book Synopsis Banach-Hilbert Spaces, Vector Measures and Group Representations by : Tsoy-Wo Ma
Download or read book Banach-Hilbert Spaces, Vector Measures and Group Representations written by Tsoy-Wo Ma and published by World Scientific. This book was released on 2002-01-01 with total page 606 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an elementary introduction to classical analysis on normed spaces, with special attention paid to fixed points, calculus, and ordinary differential equations. It contains a full treatment of vector measures on delta rings without assuming any scalar measure theory and hence should fit well into existing courses. The relation between group representations and almost periodic functions is presented. The mean values offer an infinite-dimensional analogue of measure theory on finite-dimensional Euclidean spaces. This book is ideal for beginners who want to get through the basic material as soon as possible and then do their own research immediately.
Book Synopsis Vector Integration and Stochastic Integration in Banach Spaces by : Nicolae Dinculeanu
Download or read book Vector Integration and Stochastic Integration in Banach Spaces written by Nicolae Dinculeanu and published by John Wiley & Sons. This book was released on 2011-09-28 with total page 446 pages. Available in PDF, EPUB and Kindle. Book excerpt: A breakthrough approach to the theory and applications of stochastic integration The theory of stochastic integration has become an intensely studied topic in recent years, owing to its extraordinarily successful application to financial mathematics, stochastic differential equations, and more. This book features a new measure theoretic approach to stochastic integration, opening up the field for researchers in measure and integration theory, functional analysis, probability theory, and stochastic processes. World-famous expert on vector and stochastic integration in Banach spaces Nicolae Dinculeanu compiles and consolidates information from disparate journal articles-including his own results-presenting a comprehensive, up-to-date treatment of the theory in two major parts. He first develops a general integration theory, discussing vector integration with respect to measures with finite semivariation, then applies the theory to stochastic integration in Banach spaces. Vector Integration and Stochastic Integration in Banach Spaces goes far beyond the typical treatment of the scalar case given in other books on the subject. Along with such applications of the vector integration as the Reisz representation theorem and the Stieltjes integral for functions of one or two variables with finite semivariation, it explores the emergence of new classes of summable processes that make applications possible, including square integrable martingales in Hilbert spaces and processes with integrable variation or integrable semivariation in Banach spaces. Numerous references to existing results supplement this exciting, breakthrough work.
Book Synopsis Integral Representations of Chains and Vector Measures by : Stephen Vankirk Noltie
Download or read book Integral Representations of Chains and Vector Measures written by Stephen Vankirk Noltie and published by . This book was released on 1975 with total page 210 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author :Niels da Vitoria Lobo Publisher :Springer Science & Business Media ISBN 13 :3540896880 Total Pages :1029 pages Book Rating :4.5/5 (48 download)
Book Synopsis Structural, Syntactic, and Statistical Pattern Recognition by : Niels da Vitoria Lobo
Download or read book Structural, Syntactic, and Statistical Pattern Recognition written by Niels da Vitoria Lobo and published by Springer Science & Business Media. This book was released on 2008-11-24 with total page 1029 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 12th International Workshop on Structural and Syntactic Pattern Recognition, SSPR 2008 and the 7th International Workshop on Statistical Techniques in Pattern Recognition, SPR 2008, held jointly in Orlando, FL, USA, in December 2008 as a satellite event of the 19th International Conference of Pattern Recognition, ICPR 2008. The 56 revised full papers and 42 revised poster papers presented together with the abstracts of 4 invited papers were carefully reviewed and selected from 175 submissions. The papers are organized in topical sections on graph-based methods, probabilistic and stochastic structural models for PR, image and video analysis, shape analysis, kernel methods, recognition and classification, applications, ensemble methods, feature selection, density estimation and clustering, computer vision and biometrics, pattern recognition and applications, pattern recognition, as well as feature selection and clustering.
Book Synopsis Operator Algebras Generated by Commuting Projections: A Vector Measure Approach by : Werner Ricker
Download or read book Operator Algebras Generated by Commuting Projections: A Vector Measure Approach written by Werner Ricker and published by Springer Verlag. This book was released on 1999-09-17 with total page 186 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a systematic investigation of the theory of those commutative, unital subalgebras (of bounded linear operators acting in a Banach space) which are closed for some given topology and are generated by a uniformly bounded Boolean algebra of projections. One of the main aims is to employ the methods of vector measures and integration as a unifying theme throughout. This yields proofs of several classical results which are quite different to the classical ones. This book is directed to both those wishing to learn this topic for the first time and to current experts in the field.
Book Synopsis An Introduction to Measure Theory by : Terence Tao
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.
Book Synopsis Complex Analysis and Dynamical Systems II by : Lawrence Allen Zalcman
Download or read book Complex Analysis and Dynamical Systems II written by Lawrence Allen Zalcman and published by American Mathematical Soc.. This book was released on 2005 with total page 456 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is a collection of papers reflecting the conference held in Nahariya, Israel in honor of Professor Lawrence Zalcman's sixtieth birthday. The papers, many written by leading authorities, range widely over classical complex analysis of one and several variables, differential equations, and integral geometry. Topics covered include, but are not limited to, these areas within the theory of functions of one complex variable: complex dynamics, elliptic functions, Kleinian groups, quasiconformal mappings, Tauberian theorems, univalent functions, and value distribution theory. Altogether, the papers in this volume provide a comprehensive overview of activity in complex analysis at the beginning of the twenty-first century and testify to the continuing vitality of the interplay between classical and modern analysis. It is suitable for graduate students and researchers interested in computer analysis and differential geometry. Information for our distributors: This book is co-published with Bar-Ilan University.
