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Measure And Integration Theory On Infinite Dimensional Spaces
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Book Synopsis Measure and Integration Theory on Infinite-Dimensional Spaces by :
Download or read book Measure and Integration Theory on Infinite-Dimensional Spaces written by and published by Academic Press. This book was released on 1972-10-16 with total page 439 pages. Available in PDF, EPUB and Kindle. Book excerpt: Measure and Integration Theory on Infinite-Dimensional Spaces
Book Synopsis Measure and Integration Theory on Infinite-dimensional Spaces by : Dao-xing Xia
Download or read book Measure and Integration Theory on Infinite-dimensional Spaces written by Dao-xing Xia and published by . This book was released on 1972 with total page 425 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Measures on Infinite Dimensional Spaces by : Yasuo Yamasaki
Download or read book Measures on Infinite Dimensional Spaces written by Yasuo Yamasaki and published by World Scientific. This book was released on 1985 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is based on lectures given at Yale and Kyoto Universities and provides a self-contained detailed exposition of the following subjects: 1) The construction of infinite dimensional measures, 2) Invariance and quasi-invariance of measures under translations. This book furnishes an important tool for the analysis of physical systems with infinite degrees of freedom (such as field theory, statistical physics and field dynamics) by providing material on the foundations of these problems.
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 Integration on Infinite-Dimensional Surfaces and Its Applications by : A. Uglanov
Download or read book Integration on Infinite-Dimensional Surfaces and Its Applications written by A. Uglanov and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: It seems hard to believe, but mathematicians were not interested in integration problems on infinite-dimensional nonlinear structures up to 70s of our century. At least the author is not aware of any publication concerning this theme, although as early as 1967 L. Gross mentioned that the analysis on infinite dimensional manifolds is a field of research with rather rich opportunities in his classical work [2. This prediction was brilliantly confirmed afterwards, but we shall return to this later on. In those days the integration theory in infinite dimensional linear spaces was essentially developed in the heuristic works of RP. Feynman [1], I. M. Gelfand, A. M. Yaglom [1]). The articles of J. Eells [1], J. Eells and K. D. Elworthy [1], H. -H. Kuo [1], V. Goodman [1], where the contraction of a Gaussian measure on a hypersurface, in particular, was built and the divergence theorem (the Gauss-Ostrogradskii formula) was proved, appeared only in the beginning of the 70s. In this case a Gaussian specificity was essential and it was even pointed out in a later monograph of H. -H. Kuo [3] that the surface measure for the non-Gaussian case construction problem is not simple and has not yet been solved. A. V. Skorokhod [1] and the author [6,10] offered different approaches to such a construction. Some other approaches were offered later by Yu. L. Daletskii and B. D. Maryanin [1], O. G. Smolyanov [6], N. V.
Book Synopsis Measure and Integration Theory by : Heinz Bauer
Download or read book Measure and Integration Theory written by Heinz Bauer and published by Walter de Gruyter. This book was released on 2011-04-20 with total page 249 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives a straightforward introduction to the field as it is nowadays required in many branches of analysis and especially in probability theory. The first three chapters (Measure Theory, Integration Theory, Product Measures) basically follow the clear and approved exposition given in the author's earlier book on "Probability Theory and Measure Theory". Special emphasis is laid on a complete discussion of the transformation of measures and integration with respect to the product measure, convergence theorems, parameter depending integrals, as well as the Radon-Nikodym theorem. The final chapter, essentially new and written in a clear and concise style, deals with the theory of Radon measures on Polish or locally compact spaces. With the main results being Luzin's theorem, the Riesz representation theorem, the Portmanteau theorem, and a characterization of locally compact spaces which are Polish, this chapter is a true invitation to study topological measure theory. The text addresses graduate students, who wish to learn the fundamentals in measure and integration theory as needed in modern analysis and probability theory. It will also be an important source for anyone teaching such a course.
Book Synopsis An Introduction to Infinite-Dimensional Analysis by : Giuseppe Da Prato
Download or read book An Introduction to Infinite-Dimensional Analysis written by Giuseppe Da Prato and published by Springer Science & Business Media. This book was released on 2006-08-25 with total page 217 pages. Available in PDF, EPUB and Kindle. Book excerpt: Based on well-known lectures given at Scuola Normale Superiore in Pisa, this book introduces analysis in a separable Hilbert space of infinite dimension. It starts from the definition of Gaussian measures in Hilbert spaces, concepts such as the Cameron-Martin formula, Brownian motion and Wiener integral are introduced in a simple way. These concepts are then used to illustrate basic stochastic dynamical systems and Markov semi-groups, paying attention to their long-time behavior.
Book Synopsis Gaussian Measures in Finite and Infinite Dimensions by : Daniel W. Stroock
Download or read book Gaussian Measures in Finite and Infinite Dimensions written by Daniel W. Stroock and published by . This book was released on 2023 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text provides a concise introduction, suitable for a one-semester special topics course, to the remarkable properties of Gaussian measures on both finite and infinite dimensional spaces. It begins with a brief resumé of probabilistic results in which Fourier analysis plays an essential role, and those results are then applied to derive a few basic facts about Gaussian measures on finite dimensional spaces. In anticipation of the analysis of Gaussian measures on infinite dimensional spaces, particular attention is given to those properties of Gaussian measures that are dimension independent, and Gaussian processes are constructed. The rest of the book is devoted to the study of Gaussian measures on Banach spaces. The perspective adopted is the one introduced by I. Segal and developed by L. Gross in which the Hilbert structure underlying the measure is emphasized. The contents of this book should be accessible to either undergraduate or graduate students who are interested in probability theory and have a solid background in Lebesgue integration theory and a familiarity with basic functional analysis. Although the focus is on Gaussian measures, the book introduces its readers to techniques and ideas that have applications in other contexts.
Book Synopsis Integration Theory on Infinite Dimensional Manifolds by : Hui-hsiung Kuo
Download or read book Integration Theory on Infinite Dimensional Manifolds written by Hui-hsiung Kuo and published by . This book was released on 1970 with total page 250 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Measure, Integration & Real Analysis by : Sheldon Axler
Download or read book Measure, Integration & Real Analysis written by Sheldon Axler and published by Springer Nature. This book was released on 2019-11-29 with total page 430 pages. Available in PDF, EPUB and Kindle. Book excerpt: This open access textbook welcomes students into the fundamental theory of measure, integration, and real analysis. Focusing on an accessible approach, Axler lays the foundations for further study by promoting a deep understanding of key results. Content is carefully curated to suit a single course, or two-semester sequence of courses, creating a versatile entry point for graduate studies in all areas of pure and applied mathematics. Motivated by a brief review of Riemann integration and its deficiencies, the text begins by immersing students in the concepts of measure and integration. Lebesgue measure and abstract measures are developed together, with each providing key insight into the main ideas of the other approach. Lebesgue integration links into results such as the Lebesgue Differentiation Theorem. The development of products of abstract measures leads to Lebesgue measure on Rn. Chapters on Banach spaces, Lp spaces, and Hilbert spaces showcase major results such as the Hahn–Banach Theorem, Hölder’s Inequality, and the Riesz Representation Theorem. An in-depth study of linear maps on Hilbert spaces culminates in the Spectral Theorem and Singular Value Decomposition for compact operators, with an optional interlude in real and complex measures. Building on the Hilbert space material, a chapter on Fourier analysis provides an invaluable introduction to Fourier series and the Fourier transform. The final chapter offers a taste of probability. Extensively class tested at multiple universities and written by an award-winning mathematical expositor, Measure, Integration & Real Analysis is an ideal resource for students at the start of their journey into graduate mathematics. A prerequisite of elementary undergraduate real analysis is assumed; students and instructors looking to reinforce these ideas will appreciate the electronic Supplement for Measure, Integration & Real Analysis that is freely available online. For errata and updates, visit https://measure.axler.net/
Book Synopsis Geometric Integration Theory by : Steven G. Krantz
Download or read book Geometric Integration Theory written by Steven G. Krantz and published by Springer Science & Business Media. This book was released on 2008-12-15 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Measure, Integration, and Functional Analysis by : Robert B. Ash
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 301 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.
Book Synopsis Classical and Discrete Functional Analysis with Measure Theory by : Martin Buntinas
Download or read book Classical and Discrete Functional Analysis with Measure Theory written by Martin Buntinas and published by Cambridge University Press. This book was released on 2022-01-20 with total page 471 pages. Available in PDF, EPUB and Kindle. Book excerpt: This advanced undergraduate/beginning graduate text covers measure theory and discrete aspects of functional analysis, with 760 exercises.
Author :Charalambos D. Aliprantis Publisher :Springer Science & Business Media ISBN 13 :3662030047 Total Pages :623 pages Book Rating :4.6/5 (62 download)
Book Synopsis Infinite Dimensional Analysis by : Charalambos D. Aliprantis
Download or read book Infinite Dimensional Analysis written by Charalambos D. Aliprantis and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 623 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text was born out of an advanced mathematical economics seminar at Caltech in 1989-90. We realized that the typical graduate student in mathematical economics has to be familiar with a vast amount of material that spans several traditional fields in mathematics. Much of the mate rial appears only in esoteric research monographs that are designed for specialists, not for the sort of generalist that our students need be. We hope that in a small way this text will make the material here accessible to a much broader audience. While our motivation is to present and orga nize the analytical foundations underlying modern economics and finance, this is a book of mathematics, not of economics. We mention applications to economics but present very few of them. They are there to convince economists that the material has so me relevance and to let mathematicians know that there are areas of application for these results. We feel that this text could be used for a course in analysis that would benefit math ematicians, engineers, and scientists. Most of the material we present is available elsewhere, but is scattered throughout a variety of sources and occasionally buried in obscurity. Some of our results are original (or more likely, independent rediscoveries). We have included some material that we cannot honestly say is neces sary to understand modern economic theory, but may yet prove useful in future research.
Book Synopsis Introduction to Infinite Dimensional Stochastic Analysis by : Zhi-yuan Huang
Download or read book Introduction to Infinite Dimensional Stochastic Analysis written by Zhi-yuan Huang and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: The infinite dimensional analysis as a branch of mathematical sciences was formed in the late 19th and early 20th centuries. Motivated by problems in mathematical physics, the first steps in this field were taken by V. Volterra, R. GateallX, P. Levy and M. Frechet, among others (see the preface to Levy[2]). Nevertheless, the most fruitful direction in this field is the infinite dimensional integration theory initiated by N. Wiener and A. N. Kolmogorov which is closely related to the developments of the theory of stochastic processes. It was Wiener who constructed for the first time in 1923 a probability measure on the space of all continuous functions (i. e. the Wiener measure) which provided an ideal math ematical model for Brownian motion. Then some important properties of Wiener integrals, especially the quasi-invariance of Gaussian measures, were discovered by R. Cameron and W. Martin[l, 2, 3]. In 1931, Kolmogorov[l] deduced a second partial differential equation for transition probabilities of Markov processes order with continuous trajectories (i. e. diffusion processes) and thus revealed the deep connection between theories of differential equations and stochastic processes. The stochastic analysis created by K. Ito (also independently by Gihman [1]) in the forties is essentially an infinitesimal analysis for trajectories of stochastic processes. By virtue of Ito's stochastic differential equations one can construct diffusion processes via direct probabilistic methods and treat them as function als of Brownian paths (i. e. the Wiener functionals).
Book Synopsis Lebesgue Integration on Euclidean Space by : Frank Jones
Download or read book Lebesgue Integration on Euclidean Space written by Frank Jones and published by Jones & Bartlett Learning. This book was released on 2001 with total page 626 pages. Available in PDF, EPUB and Kindle. Book excerpt: "'Lebesgue Integration on Euclidean Space' contains a concrete, intuitive, and patient derivation of Lebesgue measure and integration on Rn. It contains many exercises that are incorporated throughout the text, enabling the reader to apply immediately the new ideas that have been presented" --
Book Synopsis Measure Theory and Integration by : G De Barra
Download or read book Measure Theory and Integration written by G De Barra and published by Elsevier. This book was released on 2003-07-01 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text approaches integration via measure theory as opposed to measure theory via integration, an approach which makes it easier to grasp the subject. Apart from its central importance to pure mathematics, the material is also relevant to applied mathematics and probability, with proof of the mathematics set out clearly and in considerable detail. Numerous worked examples necessary for teaching and learning at undergraduate level constitute a strong feature of the book, and after studying statements of results of the theorems, students should be able to attempt the 300 problem exercises which test comprehension and for which detailed solutions are provided. Approaches integration via measure theory, as opposed to measure theory via integration, making it easier to understand the subject Includes numerous worked examples necessary for teaching and learning at undergraduate level Detailed solutions are provided for the 300 problem exercises which test comprehension of the theorems provided
