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Dieses Lehrbuch der Maß- und Integrationstheorie vermittelt dem Leser ein solides Basiswissen, wie es für weite Bereiche der Mathematik unerläßlich ist, insbesondere für reelle Analysis, Funktionalanalysis, Wahrscheinlichkeitstheorie und mathematische Statistik. Thematische Schwerpunkte sind Produktmaße, Fourier-Transformation, Transformationsformel, Konvergenzbegriffe, absolute Stetigkeit und Maße auf topologischen Räumen. Höhepunkt ist die Herleitung des Rieszschen Darstellungssatzes mit Hilfe eines Fortsetzungsresultats von Kisynski und der Beweis der Existenz und Eindeutigkeit des Haarschen Maßes. Der Text wird aufgelockert durch mathematikhistorische Ausflüge und Kurzporträts von Mathematikern, die zum Thema des Buches wichtige Beiträge geliefert haben. Eine Vielzahl von Übungsaufgaben vertieft den Stoff. Aus den Rezensionen: "... In diesem Buch wird die Maß- und Integrationstheorie als ein zentrales Gebiet der Mathematik dargestellt, das insbesondere für die Funktionalanalysis und die Stochastik unentbehrlich ist; es hat daher zu Recht seinen Platz in der Reihe 'Grundwissen Mathematik'. Vor allem für denjenigen, der über Grundkenntnisse bereits verfügt, ist es eine Quelle der Anregung und Bereicherung." (Zentralblatt für Mathematik und ihre Grenzgebiete, 861 (1997), 148-149) "... Das Buch ... zeugt von großer Lehrerfahrung des Autors. Es ist flüssig geschrieben, vermittelt solides Grundwissen und enthält viele Beispiele und Übungsaufgaben. Deshalb kann ich es Mathematik-Studenten aller Richtungen (einschließlich Lehramtskandidaten) zum Gebrauch neben der Vorlesung nachdrücklich empfehlen." (Zeitschrift für Analysis und ihre Anwendungen 16 (1997), 493-494).

Functions of real variables. --- Probabilities. --- Real Functions. --- Probability Theory and Stochastic Processes.

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Functions of complex variables --- Functions of complex variables. --- Complex variables --- Elliptic functions --- Functions of real variables --- Calculus

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Various generalizations of the classical concept of a convex function have been introduced, especially during the second half of the 20th century. Generalized convex functions are the many nonconvex functions which share at least one of the valuable properties of convex functions. Apart from their theoretical interest, they are often more suitable than convex functions to describe real-word problems in disciplines such as economics, engineering, management science, probability theory and in other applied sciences. More recently, generalized monotone maps which are closely related to generalized convex functions have also been studied extensively. While initial efforts to generalize convexity and monotonicity were limited to only a few research centers, today there are numerous researchers throughout the world and in various disciplines engaged in theoretical and applied studies of generalized convexity/monotonicity (see http://www.genconv.org). The Handbook offers a systematic and thorough exposition of the theory and applications of the various aspects of generalized convexity and generalized monotonicity. It is aimed at the non-expert, for whom it provides a detailed introduction, as well as at the expert who seeks to learn about the latest developments and references in his research area. Results in this fast growing field are contained in a large number of scientific papers which appeared in a variety of professional journals, partially due to the interdisciplinary nature of the subject matter. Each of its fourteen chapters is written by leading experts of the respective research area starting from the very basics and moving on to the state of the art of the subject. Each chapter is complemented by a comprehensive bibliography which will assist the non-expert and expert alike.

Convex functions. --- Monotonic functions. --- Functions, Monotonic --- Functions of real variables --- Functions, Convex --- Convex functions --- Monotonic functions --- Mathematics. --- Real Functions. --- Game Theory, Economics, Social and Behav. Sciences. --- Operations Research, Management Science. --- Math --- Science --- Functions of real variables. --- Game theory. --- Operations research. --- Management science. --- Games, Theory of --- Theory of games --- Mathematical models --- Mathematics --- Real variables --- Functions of complex variables --- Quantitative business analysis --- Management --- Problem solving --- Operations research --- Statistical decision --- Operational analysis --- Operational research --- Industrial engineering --- Management science --- Research --- System theory

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Complex geometry studies (compact) complex manifolds. It discusses algebraic as well as metric aspects. The subject is on the crossroad of algebraic and differential geometry. Recent developments in string theory have made it an highly attractive area, both for mathematicians and theoretical physicists. The author’s goal is to provide an easily accessible introduction to the subject. The book contains detailed accounts of the basic concepts and the many exercises illustrate the theory. Appendices to various chapters allow an outlook to recent research directions. Daniel Huybrechts is currently Professor of Mathematics at the University Denis Diderot in Paris.

Geometry, Differential. --- Geometry, Algebraic. --- Manifolds (Mathematics) --- Geometry, Differential --- Topology --- Algebraic geometry --- Geometry --- Differential geometry --- Geometry, Algebraic --- 512.7 --- 512.7 Algebraic geometry. Commutative rings and algebras --- Algebraic geometry. Commutative rings and algebras --- Geometry, algebraic. --- Functions of complex variables. --- Algebraic Geometry. --- Functions of a Complex Variable. --- Complex variables --- Elliptic functions --- Functions of real variables --- Komplexe Geometrie. --- Complexe manifolds. --- Algebraïsche meetkunde. --- Algebraic geometry.

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This volume is dedicated to the memory of the outstanding mathematician S.Ya. Khavinson. It begins with an expository paper by V.P. Havin presenting a comprehensive survey of Khavinson's works as well as certain biographical material. The complete bibliography following this paper has not previously been published anywhere. It consists of 163 items; a considerable part of these cannot be found in easily accessible sources. The book also contains a series of photographs and twelve original peer-reviewed research and expository papers by leading mathematicians worldwide, including the joint paper by S.Ya. Khavinson and T.S. Kuzina (the last publication of S.Ya. Khavinson). The main topics covered are extremal problems for various classes of functions, approximation problems, Cauchy integral and analytic capacity, Cantor sets, meromorphic functions (value distribution, quasinormal families), Carathéodory inequality, integral representation of functions, and the shift operator. The book is suitable for graduate students and researchers interested in analysis.

Functions of complex variables. --- Mathematical analysis. --- Khavinson, S. I͡A. --- Complex variables --- Elliptic functions --- Functions of real variables --- 517.1 Mathematical analysis --- Mathematical analysis --- Khavinson, Semen Yakovlevich --- Khavinson, S. Ya. --- Khavinson, Semyon Yakovlevich --- Mathematics. --- Operator theory. --- Functions of a Complex Variable. --- Approximations and Expansions. --- Operator Theory. --- Functional analysis --- Math --- Science --- Approximation theory. --- Theory of approximation --- Functions --- Polynomials --- Chebyshev systems --- Khavinson, S. I︠A︡.