A Course On Integration Theory
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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 Course On Integration Theory
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Author : K. Chandrasekharan
language : en
Publisher:
Release Date : 1996
A Course On Integration Theory written by K. Chandrasekharan and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996 with Integrals, Generalized categories.
Integration Theory
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Author : Martin Väth
language : en
Publisher:
Release Date : 2002
Integration Theory written by Martin Väth and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with categories.
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.
Essentials Of Integration Theory For Analysis
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Author : Daniel W. Stroock
language : en
Publisher: Springer Nature
Release Date : 2020-11-24
Essentials Of Integration Theory For Analysis written by Daniel W. Stroock and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-11-24 with Mathematics categories.
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.
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 : 2013-03-14
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 2013-03-14 with Mathematics categories.
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".
Integration Theory
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Author : Martin Väth
language : en
Publisher: World Scientific Publishing Company Incorporated
Release Date : 2002-01-01
Integration Theory written by Martin Väth and has been published by World Scientific Publishing Company Incorporated this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-01-01 with Mathematics categories.
This book presents a very general approach to integration theory, as well as some advanced topics of the theory. It includes some new results but is also a self-contained introduction suitable for a graduate student doing self-study or an advanced course on integration theory. The book is divided into two parts. In the first part, integration theory is developed from the beginning in a general setting and for vector-valued functions which can hardly be found in other textbooks. The second part covers various topics related to integration theory, such as spaces of measurable functions, convolutions, famous paradoxes in connection with set theory, and extensions of formulas from elementary calculus to the setting of the Lebesgue integral.
Geometric Integration Theory
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Author : Steven G. Krantz
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-12-15
Geometric Integration Theory written by Steven G. Krantz 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 2008-12-15 with Mathematics categories.
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.
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.
Integration Theory Measure And Integral
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Author : Corneliu Constantinescu
language : en
Publisher:
Release Date : 1985
Integration Theory Measure And Integral written by Corneliu Constantinescu and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1985 with categories.