Real Analysis

Author: J Yeh
Publisher: World Scientific Publishing Company
ISBN: 9814578568
Format: PDF, Mobi
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This book presents a unified treatise of the theory of measure and integration. In the setting of a general measure space, every concept is defined precisely and every theorem is presented with a clear and complete proof with all the relevant details. Counter-examples are provided to show that certain conditions in the hypothesis of a theorem cannot be simply dropped. The dependence of a theorem on earlier theorems is explicitly indicated in the proof, not only to facilitate reading but also to delineate the structure of the theory. The precision and clarity of presentation make the book an ideal textbook for a graduate course in real analysis while the wealth of topics treated also make the book a valuable reference work for mathematicians. The book is also very helpful to graduate students in statistics and electrical engineering, two disciplines that apply measure theory.

Problems and Proofs in Real Analysis

Author: J Yeh
Publisher: World Scientific Publishing Company
ISBN: 9814578525
Format: PDF, Mobi
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This volume consists of the proofs of 391 problems in Real Analysis: Theory of Measure and Integration (3rd Edition). Most of the problems in Real Analysis are not mere applications of theorems proved in the book but rather extensions of the proven theorems or related theorems. Proving these problems tests the depth of understanding of the theorems in the main text. This volume will be especially helpful to those who read Real Analysis in self-study and have no easy access to an instructor or an advisor.

Measure Theory

Author: Vladimir I. Bogachev
Publisher: Springer Science & Business Media
ISBN: 3540345140
Format: PDF, ePub, Mobi
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This book giving an exposition of the foundations of modern measure theory offers three levels of presentation: a standard university graduate course, an advanced study containing some complements to the basic course, and, finally, more specialized topics partly covered by more than 850 exercises with detailed hints and references. Bibliographical comments and an extensive bibliography with 2000 works covering more than a century are provided.

An Introduction to Nonlinear Analysis Theory

Author: Zdzisław Denkowski
Publisher: Springer Science & Business Media
ISBN: 9780306473920
Format: PDF, Docs
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An Introduction to Nonlinear Analysis: Theory is an overview of some basic, important aspects of Nonlinear Analysis, with an emphasis on those not included in the classical treatment of the field. Today Nonlinear Analysis is a very prolific part of modern mathematical analysis, with fascinating theory and many different applications ranging from mathematical physics and engineering to social sciences and economics. Topics covered in this book include the necessary background material from topology, measure theory and functional analysis (Banach space theory). The text also deals with multivalued analysis and basic features of nonsmooth analysis, providing a solid background for the more applications-oriented material of the book An Introduction to Nonlinear Analysis: Applications by the same authors. The book is self-contained and accessible to the newcomer, complete with numerous examples, exercises and solutions. It is a valuable tool, not only for specialists in the field interested in technical details, but also for scientists entering Nonlinear Analysis in search of promising directions for research.

A First Course in Functional Analysis

Author: Rabindranath Sen
Publisher: Anthem Press
ISBN: 1783083247
Format: PDF, Kindle
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This book provides the reader with a comprehensive introduction to functional analysis. Topics include normed linear and Hilbert spaces, the Hahn-Banach theorem, the closed graph theorem, the open mapping theorem, linear operator theory, the spectral theory, and a brief introduction to the Lebesgue measure. The book explains the motivation for the development of these theories, and applications that illustrate the theories in action. Applications in optimal control theory, variational problems, wavelet analysis and dynamical systems are also highlighted. ‘A First Course in Functional Analysis’ will serve as a ready reference to students not only of mathematics, but also of allied subjects in applied mathematics, physics, statistics and engineering.

Reelle und Komplexe Analysis

Author: Walter Rudin
Publisher: Walter de Gruyter
ISBN: 9783486591866
Format: PDF
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Besonderen Wert legt Rudin darauf, dem Leser die Zusammenhänge unterschiedlicher Bereiche der Analysis zu vermitteln und so die Grundlage für ein umfassenderes Verständnis zu schaffen. Das Werk zeichnet sich durch seine wissenschaftliche Prägnanz und Genauigkeit aus und hat damit die Entwicklung der modernen Analysis in nachhaltiger Art und Weise beeinflusst. Der "Baby-Rudin" gehört weltweit zu den beliebtesten Lehrbüchern der Analysis und ist in 13 Sprachen übersetzt. 1993 wurde es mit dem renommierten Steele Prize for Mathematical Exposition der American Mathematical Society ausgezeichnet. Übersetzt von Uwe Krieg.

Wissen im Diskurs

Author: Laura Kajetzke
Publisher: Springer-Verlag
ISBN: 3531907816
Format: PDF, Mobi
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In dieser Arbeit werden die theoretischen Perspektiven Pierre Bourdieus und Michel Foucaults einer wissenssoziologischen Lesart unterzogen: Wie verhalten sich Foucaults Konzepte Wissen, Macht, Subjekt, Diskurs und Dispositiv zu Bourdieus Konzepten von Wissen, Habitus, Feld und den Kapitalarten? Die Autorin zeigt anhand einer Analyse der printmedialen PISA-Berichterstattung, wie man mithilfe eines solchen Vergleichs Leitfragen und ein diskursanalytisches Vorgehen entwickeln kann.