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Author: Kenneth Kuttler
Publisher: CRC Press
ISBN: 1351360000
Category : Mathematics
Languages : en
Pages : 584
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Book Description
Modern Analysis provides coverage of real and abstract analysis, offering a sensible introduction to functional analysis as well as a thorough discussion of measure theory, Lebesgue integration, and related topics. This significant study clearly and distinctively presents the teaching and research literature of graduate analysis: Providing a fundamental, modern approach to measure theory Investigating advanced material on the Bochner integral, geometric theory, and major theorems in Fourier Analysis Rn, including the theory of singular integrals and Milhin's theorem - material that does not appear in textbooks Offering exceptionally concise and cardinal versions of all the main theorems about characteristic functions Containing an original examination of sufficient statistics, based on the general theory of Radon measures With an ambitious scope, this resource unifies various topics into one volume succinctly and completely. The contents span basic measure theory in an abstract and concrete form, material on classic linear functional analysis, probability, and some major results used in the theory of partial differential equations. Two different proofs of the central limit theorem are examined as well as a straightforward approach to conditional probability and expectation. Modern Analysis provides ample and well-constructed exercises and examples. Introductory topology is included to help the reader understand such items as the Riesz theorem, detailing its proofs and statements. This work will help readers apply measure theory to probability theory, guiding them to understand the theorems rather than merely follow directions.
Author: Kenneth Kuttler
Publisher: CRC Press
ISBN: 1351360000
Category : Mathematics
Languages : en
Pages : 584
Get Book
Book Description
Modern Analysis provides coverage of real and abstract analysis, offering a sensible introduction to functional analysis as well as a thorough discussion of measure theory, Lebesgue integration, and related topics. This significant study clearly and distinctively presents the teaching and research literature of graduate analysis: Providing a fundamental, modern approach to measure theory Investigating advanced material on the Bochner integral, geometric theory, and major theorems in Fourier Analysis Rn, including the theory of singular integrals and Milhin's theorem - material that does not appear in textbooks Offering exceptionally concise and cardinal versions of all the main theorems about characteristic functions Containing an original examination of sufficient statistics, based on the general theory of Radon measures With an ambitious scope, this resource unifies various topics into one volume succinctly and completely. The contents span basic measure theory in an abstract and concrete form, material on classic linear functional analysis, probability, and some major results used in the theory of partial differential equations. Two different proofs of the central limit theorem are examined as well as a straightforward approach to conditional probability and expectation. Modern Analysis provides ample and well-constructed exercises and examples. Introductory topology is included to help the reader understand such items as the Riesz theorem, detailing its proofs and statements. This work will help readers apply measure theory to probability theory, guiding them to understand the theorems rather than merely follow directions.
Author: Kenneth Kuttler
Publisher: CRC Press
ISBN: 1351359991
Category : Mathematics
Languages : en
Pages : 438
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Book Description
Modern Analysis provides coverage of real and abstract analysis, offering a sensible introduction to functional analysis as well as a thorough discussion of measure theory, Lebesgue integration, and related topics. This significant study clearly and distinctively presents the teaching and research literature of graduate analysis: Providing a fundamental, modern approach to measure theory Investigating advanced material on the Bochner integral, geometric theory, and major theorems in Fourier Analysis Rn, including the theory of singular integrals and Milhin's theorem - material that does not appear in textbooks Offering exceptionally concise and cardinal versions of all the main theorems about characteristic functions Containing an original examination of sufficient statistics, based on the general theory of Radon measures With an ambitious scope, this resource unifies various topics into one volume succinctly and completely. The contents span basic measure theory in an abstract and concrete form, material on classic linear functional analysis, probability, and some major results used in the theory of partial differential equations. Two different proofs of the central limit theorem are examined as well as a straightforward approach to conditional probability and expectation. Modern Analysis provides ample and well-constructed exercises and examples. Introductory topology is included to help the reader understand such items as the Riesz theorem, detailing its proofs and statements. This work will help readers apply measure theory to probability theory, guiding them to understand the theorems rather than merely follow directions.
Author: Gerald B. Folland
Publisher: John Wiley & Sons
ISBN: 1118626397
Category : Mathematics
Languages : en
Pages : 368
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Book Description
An in-depth look at real analysis and its applications-now expanded and revised. This new edition of the widely used analysis book continues to cover real analysis in greater detail and at a more advanced level than most books on the subject. Encompassing several subjects that underlie much of modern analysis, the book focuses on measure and integration theory, point set topology, and the basics of functional analysis. It illustrates the use of the general theories and introduces readers to other branches of analysis such as Fourier analysis, distribution theory, and probability theory. This edition is bolstered in content as well as in scope-extending its usefulness to students outside of pure analysis as well as those interested in dynamical systems. The numerous exercises, extensive bibliography, and review chapter on sets and metric spaces make Real Analysis: Modern Techniques and Their Applications, Second Edition invaluable for students in graduate-level analysis courses. New features include: * Revised material on the n-dimensional Lebesgue integral. * An improved proof of Tychonoff's theorem. * Expanded material on Fourier analysis. * A newly written chapter devoted to distributions and differential equations. * Updated material on Hausdorff dimension and fractal dimension.
Author: Ahmet KADİROĞLU
Publisher: Livre de Lyon
ISBN: 2382365641
Category : Business & Economics
Languages : en
Pages : 213
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Book Description
Economics and Administration Sciences Modern Analysis and Researches
Author: John J. Benedetto
Publisher: Springer Science & Business Media
ISBN: 0817646566
Category : Mathematics
Languages : en
Pages : 589
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Book Description
This textbook and treatise begins with classical real variables, develops the Lebesgue theory abstractly and for Euclidean space, and analyzes the structure of measures. The authors' vision of modern real analysis is seen in their fascinating historical commentary and perspectives with other fields. There are comprehensive treatments of the role of absolute continuity, the evolution of the Riesz representation theorem to Radon measures and distribution theory, weak convergence of measures and the Dieudonné–Grothendieck theorem, modern differentiation theory, fractals and self-similarity, rearrangements and maximal functions, and surface and Hausdorff measures. There are hundreds of illuminating exercises, and extensive, focused appendices on functional and Fourier analysis. The presentation is ideal for the classroom, self-study, or professional reference.
Author: E. T. Whittaker
Publisher: Cambridge University Press
ISBN: 9780521588072
Category : Mathematics
Languages : en
Pages : 620
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Book Description
This classic text is known to and used by thousands of mathematicians and students of mathematics thorughout the world. It gives an introduction to the general theory of infinite processes and of analytic functions together with an account of the principle transcendental functions.
Author: Ron S. Kenett
Publisher: John Wiley & Sons
ISBN: 0470971282
Category : Mathematics
Languages : en
Pages : 533
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Book Description
Customer survey studies deals with customers, consumers and user satisfaction from a product or service. In practice, many of the customer surveys conducted by business and industry are analyzed in a very simple way, without using models or statistical methods. Typical reports include descriptive statistics and basic graphical displays. As demonstrated in this book, integrating such basic analysis with more advanced tools, provides insights on non-obvious patterns and important relationships between the survey variables. This knowledge can significantly affect the conclusions derived from a survey. Key features: Provides an integrated, case-studies based approach to analysing customer survey data. Presents a general introduction to customer surveys, within an organization’s business cycle. Contains classical techniques with modern and non standard tools. Focuses on probabilistic techniques from the area of statistics/data analysis and covers all major recent developments. Accompanied by a supporting website containing datasets and R scripts. Customer survey specialists, quality managers and market researchers will benefit from this book as well as specialists in marketing, data mining and business intelligence fields.
Author: Grace M. Davidson
Publisher: ASM International
ISBN: 1615030824
Category : Technology & Engineering
Languages : en
Pages : 310
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Book Description
Author: Elliott H. Lieb
Publisher: American Mathematical Soc.
ISBN: 0821827839
Category : Analysis
Languages : en
Pages : 378
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Book Description
This course in real analysis begins with the usual measure theory, then brings the reader quickly to a level where a wider than usual range of topics can be appreciated. Topics covered include Lp- spaces, rearrangement inequalities, sharp integral inequalities, distribution theory, Fourier analysis, potential theory, and Sobolev spaces. To illustrate these topics, there is a chapter on the calculus of variations, with examples from mathematical physics, as well as a chapter on eigenvalue problems (new to this edition). For graduate students of mathematics, and for students of the natural sciences and engineering who want to learn tools of real analysis. Assumes a previous course in calculus. Lieb is affiliated with Princeton University. Loss is affiliated with Georgia Institute of Technology. c. Book News Inc.
Author: Nicholas J. Daras
Publisher: Springer
ISBN: 3319743252
Category : Mathematics
Languages : en
Pages : 521
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Book Description
A variety of modern research in analysis and discrete mathematics is provided in this book along with applications in cryptographic methods and information security, in order to explore new techniques, methods, and problems for further investigation. Distinguished researchers and scientists in analysis and discrete mathematics present their research. Graduate students, scientists and engineers, interested in a broad spectrum of current theories, methods, and applications in interdisciplinary fields will find this book invaluable.
