Download or read book Geometric Integration Theory written by Hassler Whitney and published by Princeton University Press. This book was released on 2015-12-08 with total page 404 pages. Available in PDF, EPUB and Kindle. Book excerpt: A complete theory of integration as it appears in geometric and physical problems must include integration over oriented r-dimensional domains in n-space; both the integrand and the domain may be variable. This is the primary subject matter of the present book, designed to bring out the underlying geometric and analytic ideas and to give clear and complete proofs of the basic theorems. Originally published in 1957. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.
Download or read book A Modern Theory of Integration written by Robert G. Bartle and published by American Mathematical Soc.. This book was released on 2001-03-21 with total page 480 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of integration is one of the twin pillars on which analysis is built. The first version of integration that students see is the Riemann integral. Later, graduate students learn that the Lebesgue integral is ``better'' because it removes some restrictions on the integrands and the domains over which we integrate. However, there are still drawbacks to Lebesgue integration, for instance, dealing with the Fundamental Theorem of Calculus, or with ``improper'' integrals. This book is an introduction to a relatively new theory of the integral (called the ``generalized Riemann integral'' or the ``Henstock-Kurzweil integral'') that corrects the defects in the classical Riemann theory and both simplifies and extends the Lebesgue theory of integration. Although this integral includes that of Lebesgue, its definition is very close to the Riemann integral that is familiar to students from calculus. One virtue of the new approach is that no measure theory and virtually no topology is required. Indeed, the book includes a study of measure theory as an application of the integral. Part 1 fully develops the theory of the integral of functions defined on a compact interval. This restriction on the domain is not necessary, but it is the case of most interest and does not exhibit some of the technical problems that can impede the reader's understanding. Part 2 shows how this theory extends to functions defined on the whole real line. The theory of Lebesgue measure from the integral is then developed, and the author makes a connection with some of the traditional approaches to the Lebesgue integral. Thus, readers are given full exposure to the main classical results. The text is suitable for a first-year graduate course, although much of it can be readily mastered by advanced undergraduate students. Included are many examples and a very rich collection of exercises. There are partial solutions to approximately one-third of the exercises. A complete solutions manual is available separately.
Download or read book A Course on Integration Theory written by Nicolas Lerner and published by Springer. This book was released on 2014-07-09 with total page 504 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook provides a detailed treatment of abstract integration theory, construction of the Lebesgue measure via the Riesz-Markov Theorem and also via the Carathéodory Theorem. It also includes some elementary properties of Hausdorff measures as well as the basic properties of spaces of integrable functions and standard theorems on integrals depending on a parameter. Integration on a product space, change of variables formulas as well as the construction and study of classical Cantor sets are treated in detail. Classical convolution inequalities, such as Young's inequality and Hardy-Littlewood-Sobolev inequality are proven. The Radon-Nikodym theorem, notions of harmonic analysis, classical inequalities and interpolation theorems, including Marcinkiewicz's theorem, the definition of Lebesgue points and Lebesgue differentiation theorem are further topics included. A detailed appendix provides the reader with various elements of elementary mathematics, such as a discussion around the calculation of antiderivatives or the Gamma function. The appendix also provides more advanced material such as some basic properties of cardinals and ordinals which are useful in the study of measurability.
Download or read book Essentials of Integration Theory for Analysis written by Daniel W. Stroock and published by Springer Nature. This book was released on 2020-11-24 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: When the first edition of this textbook published in 2011, it constituted a substantial revision of the best-selling Birkhäuser title by the same author, A Concise Introduction to the Theory of Integration. Appropriate as a primary text for a one-semester graduate course in integration theory, this GTM is also useful for independent study. A complete solutions manual is available for instructors who adopt the text for their courses. This second edition has been revised as follows: §2.2.5 and §8.3 have been substantially reworked. New topics have been added. As an application of the material about Hermite functions in §7.3.2, the author has added a brief introduction to Schwartz's theory of tempered distributions in §7.3.4. Section §7.4 is entirely new and contains applications, including the Central Limit Theorem, of Fourier analysis to measures. Related to this are subsections §8.2.5 and §8.2.6, where Lévy's Continuity Theorem and Bochner's characterization of the Fourier transforms of Borel probability on RN are proven. Subsection 8.1.2 is new and contains a proof of the Hahn Decomposition Theorem. Finally, there are several new exercises, some covering material from the original edition and others based on newly added material.
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.
Download or read book Convex Integration Theory written by David Spring and published by Springer Science & Business Media. This book was released on 2010-12-02 with total page 219 pages. Available in PDF, EPUB and Kindle. Book excerpt: §1. Historical Remarks Convex Integration theory, ?rst introduced by M. Gromov [17], is one of three general methods in immersion-theoretic topology for solving a broad range of problems in geometry and topology. The other methods are: (i) Removal of Singularities, introduced by M. Gromov and Y. Eliashberg [8]; (ii) the covering homotopy method which, following M. Gromov’s thesis [16], is also referred to as the method of sheaves. The covering homotopy method is due originally to S. Smale [36] who proved a crucial covering homotopy result in order to solve the classi?cation problem for immersions of spheres in Euclidean space. These general methods are not linearly related in the sense that succ- sive methods subsumed the previous methods. Each method has its own distinct foundation, based on an independent geometrical or analytical insight. Con- quently, each method has a range of applications to problems in topology that are best suited to its particular insight. For example, a distinguishing feature of ConvexIntegrationtheoryisthatitappliestosolveclosed relationsinjetspaces, including certain general classes of underdetermined non-linear systems of par- 1 tial di?erential equations. As a case of interest, the Nash-Kuiper C -isometric immersion theorem can be reformulated and proved using Convex Integration theory (cf. Gromov [18]). No such results on closed relations in jet spaces can be proved by means of the other two methods. On the other hand, many classical results in immersion-theoretic topology, such as the classi?cation of immersions, are provable by all three methods.
Download or read book Some integration theory written by Roberto Montano and published by . This book was released on 1971 with total page 40 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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.
Download or read book Measure and Integration written by Heinz König and published by Springer Science & Business Media. This book was released on 1997 with total page 277 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book aims at restructuring some fundamentals in measure and integration theory. It centers around the ubiquitous task to produce appropriate contents and measures from more primitive data like elementary contents and elementary integrals. It develops the new approach started around 1970 by Topsoe and others into a systematic theory. The theory is much more powerful than the traditional means and has striking implications all over measure theory and beyond.
Download or read book The Theory of Measures and Integration written by Eric M. Vestrup and published by John Wiley & Sons. This book was released on 2009-09-25 with total page 622 pages. Available in PDF, EPUB and Kindle. Book excerpt: An accessible, clearly organized survey of the basic topics of measure theory for students and researchers in mathematics, statistics, and physics In order to fully understand and appreciate advanced probability, analysis, and advanced mathematical statistics, a rudimentary knowledge of measure theory and like subjects must first be obtained. The Theory of Measures and Integration illuminates the fundamental ideas of the subject-fascinating in their own right-for both students and researchers, providing a useful theoretical background as well as a solid foundation for further inquiry. Eric Vestrup's patient and measured text presents the major results of classical measure and integration theory in a clear and rigorous fashion. Besides offering the mainstream fare, the author also offers detailed discussions of extensions, the structure of Borel and Lebesgue sets, set-theoretic considerations, the Riesz representation theorem, and the Hardy-Littlewood theorem, among other topics, employing a clear presentation style that is both evenly paced and user-friendly. Chapters include: * Measurable Functions * The Lp Spaces * The Radon-Nikodym Theorem * Products of Two Measure Spaces * Arbitrary Products of Measure Spaces Sections conclude with exercises that range in difficulty between easy "finger exercises"and substantial and independent points of interest. These more difficult exercises are accompanied by detailed hints and outlines. They demonstrate optional side paths in the subject as well as alternative ways of presenting the mainstream topics. In writing his proofs and notation, Vestrup targets the person who wants all of the details shown up front. Ideal for graduate students in mathematics, statistics, and physics, as well as strong undergraduates in these disciplines and practicing researchers, The Theory of Measures and Integration proves both an able primary text for a real analysis sequence with a focus on measure theory and a helpful background text for advanced courses in probability and statistics.
Download or read book European Integration Theory written by Antje Wiener and published by Oxford University Press. This book was released on 2019-12-19 with total page 355 pages. Available in PDF, EPUB and Kindle. Book excerpt: With coverage of both traditional and critical theories and approaches to European integration and their application, this is the most comprehensive textbook on European integration theory and an essential guide for all students and scholars interested in the subject. Throughout the text, a team of leading international scholars demonstrate the current relevance of integration theory as they apply these approaches to real-world developments and crises in the contemporary European Union.
Download or read book A Concise Introduction to the Theory of Integration written by Daniel W. Stroock and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 193 pages. Available in PDF, EPUB and Kindle. Book excerpt: This little book is the outgrowth of a one semester course which I have taught for each of the past four years at M. 1. T. Although this class used to be one of the standard courses taken by essentially every first year gradu ate student of mathematics, in recent years (at least in those when I was the instructor), the clientele has shifted from first year graduate students of mathematics to more advanced graduate students in other disciplines. In fact, the majority of my students have been from departments of engi neering (especially electrical engineering) and most of the rest have been economists. Whether this state of affairs is a reflection on my teaching, the increased importance of mathematical analysis in other disciplines, the superior undergraduate preparation of students coming to M. 1. T in mathematics, or simply the lack of enthusiasm that these students have for analysis, I have preferred not to examine too closely. On the other hand, the situation did force me to do a certain amount of thinking about what constitutes an appropriate course for a group of non-mathematicians who are courageous (foolish?) enough to sign up for an introduction to in tegration theory offered by the department of mathematics. In particular, I had to figure out what to do about that vast body of material which, in standard mathematics offerings, is "assumed to have been covered in your advanced calculus course".
Download or read book Integration Theory written by Augustus J.E.M. Janssen and published by Springer. This book was released on 2006-12-08 with total page 229 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Measure Theory and Integration written by Michael Eugene Taylor and published by American Mathematical Soc.. This book was released on 2006 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Stochastic Integration Theory written by Peter Medvegyev and published by Oxford University Press, USA. This book was released on 2007-07-26 with total page 629 pages. Available in PDF, EPUB and Kindle. Book excerpt: This graduate level text covers the theory of stochastic integration, an important area of Mathematics that has a wide range of applications, including financial mathematics and signal processing. Aimed at graduate students in Mathematics, Statistics, Probability, Mathematical Finance, and Economics, the book not only covers the theory of the stochastic integral in great depth but also presents the associated theory (martingales, Levy processes) and important examples (Brownianmotion, Poisson process).
Download or read book Classical and Modern Integration Theories written by Ivan N. Pesin and published by Academic Press. This book was released on 2014-07-03 with total page 218 pages. Available in PDF, EPUB and Kindle. Book excerpt: Classical and Modern Integration Theories discusses classical integration theory, particularly that part of the theory directly associated with the problems of area. The book reviews the history and the determination of primitive functions, beginning from Cauchy to Daniell. The text describes Cauchy's definition of an integral, Riemann's definition of the R-integral, the upper and lower Darboux integrals. The book also reviews the origin of the Lebesgue-Young integration theory, and Borel's postulates that define measures of sets. W.H. Young's work provides a construction of the integral equivalent to Lebesque's construction with a different generalization of integrals leading to different approaches in solutions. Young's investigations aim at generalizing the notion of length for arbitrary sets by means of a process which is more general than Borel's postulates. The text notes that the Lebesgue measure is the unique solution of the measure problem for the class of L-measurable sets. The book also describes further modifications made into the Lebesgue definition of the integral by Riesz, Pierpont, Denjoy, Borel, and Young. These modifications bring the Lebesgue definition of the integral closer to the Riemann or Darboux definitions, as well as to have it associated with the concepts of classical analysis. The book can benefit mathematicians, students, and professors in calculus or readers interested in the history of classical mathematics.
Download or read book General Theory of Functions and Integration written by Angus E. Taylor and published by Courier Corporation. This book was released on 2012-05-24 with total page 456 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presenting the various approaches to the study of integration, a well-known mathematics professor brings together in one volume "a blend of the particular and the general, of the concrete and the abstract." This volume is suitable for advanced undergraduates and graduate courses as well as for independent study. 1966 edition.
