A Course On Integration Theory
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A Course On Integration Theory
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Author : K. Chandrasekharan
language : en
Publisher: Springer
Release Date : 1996-01-01
A Course On Integration Theory written by K. Chandrasekharan and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996-01-01 with Mathematics categories.
A Course On Integration Theory
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Author : Nicolas Lerner
language : en
Publisher: Springer
Release Date : 2014-07-09
A Course On Integration Theory written by Nicolas Lerner and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-07-09 with Mathematics categories.
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.
A Modern Theory Of Integration
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Author : Robert G. Bartle
language : en
Publisher: American Mathematical Society
Release Date : 2024-10-25
A Modern Theory Of Integration written by Robert G. Bartle and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-10-25 with Mathematics categories.
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.
A Concise Introduction To The Theory Of Integration
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Author : Daniel W. Stroock
language : en
Publisher: Springer Science & Business Media
Release Date : 1998-12-23
A Concise Introduction To The Theory Of Integration written by Daniel W. Stroock and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-12-23 with Mathematics categories.
Designed for the analyst, physicist, engineer, or economist, provides such readers with most of the measure theory they will ever need. Emphasis is on the concrete aspects of the subject. Subjects include classical theory, Lebesgue's measure, Lebesgue integration, products of measures, changes of variable, some basic inequalities, and abstract theory. Annotation copyright by Book News, Inc., Portland, OR
Theories Of Integration
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Author : Douglas S. Kurtz
language : en
Publisher: World Scientific
Release Date : 2004
Theories Of Integration written by Douglas S. Kurtz and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Mathematics categories.
This book presents a historical development of the integration theories of Riemann, Lebesgue, Henstock-Kurzweil, and McShane, showing how new theories of integration were developed to solve problems that earlier theories could not handle. It develops the basic properties of each integral in detail and provides comparisons of the different integrals. The chapters covering each integral are essentially independent and can be used separately in teaching a portion of an introductory course on real analysis. There is a sufficient supply of exercises to make the book useful as a textbook.
Measure And Integration
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Author : Heinz König
language : en
Publisher: Springer Science & Business Media
Release Date : 1997
Measure And Integration written by Heinz König and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997 with Mathematics categories.
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.
Measure And Integration Theory
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Author : Heinz Bauer
language : en
Publisher: Walter de Gruyter
Release Date : 2011-04-20
Measure And Integration Theory written by Heinz Bauer and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-04-20 with Mathematics categories.
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.
A Course In Functional Analysis And Measure Theory
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Author : Vladimir Kadets
language : en
Publisher: Springer
Release Date : 2018-07-10
A Course In Functional Analysis And Measure Theory written by Vladimir Kadets and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-07-10 with Mathematics categories.
Written by an expert on the topic and experienced lecturer, this textbook provides an elegant, self-contained introduction to functional analysis, including several advanced topics and applications to harmonic analysis. Starting from basic topics before proceeding to more advanced material, the book covers measure and integration theory, classical Banach and Hilbert space theory, spectral theory for bounded operators, fixed point theory, Schauder bases, the Riesz-Thorin interpolation theorem for operators, as well as topics in duality and convexity theory. Aimed at advanced undergraduate and graduate students, this book is suitable for both introductory and more advanced courses in functional analysis. Including over 1500 exercises of varying difficulty and various motivational and historical remarks, the book can be used for self-study and alongside lecture courses.
Measure Theory And Integration
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Author : Michael Eugene Taylor
language : en
Publisher: American Mathematical Soc.
Release Date :
Measure Theory And Integration written by Michael Eugene Taylor and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on with Mathematics categories.
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.
A Course On Integral Equations
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Author : A. C. Pipkin
language : en
Publisher: Springer Science & Business Media
Release Date : 1991-09-12
A Course On Integral Equations written by A. C. Pipkin and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991-09-12 with Mathematics categories.
This book is based on a one semester course for graduate students in physical sciences and applied mathemat- ics. Not detailed mathematical background is needed but the student should be familiar with the theory of analytic functions of a complex variable. Since the course is problem-solving rather than theorem proving, the main requirement is that the student should be willing to work out a large number of specific examples. The course is divided about equally into three parts, where the first part is mostly theoretical and the remaining two parts emphasize on problem solving.