Geometry of Sets and Measures in Euclidean Spaces PDF Download

Author: Pertti Mattila
Publisher: Cambridge University Press
ISBN: 9780521655958
Category : Mathematics
Languages : en
Pages : 360

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Book Description
This book studies the geometric properties of general sets and measures in euclidean space.

Author: Alexander S. Kechris
Publisher: Cambridge University Press
ISBN: 1316873633
Category : Mathematics
Languages : en
Pages : 318

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Book Description
The proceedings of the Los Angeles Caltech-UCLA 'Cabal Seminar' were originally published in the 1970s and 1980s. Large Cardinals, Determinacy and Other Topics is the final volume in a series of four books collecting the seminal papers from the original volumes together with extensive unpublished material, new papers on related topics and discussion of research developments since the publication of the original volumes. This final volume contains Parts VII and VIII of the series. Part VII focuses on 'Extensions of AD, models with choice', while Part VIII ('Other topics') collects material important to the Cabal that does not fit neatly into one of its main themes. These four volumes will be a necessary part of the book collection of every set theorist.

Author: C. Dellacherie
Publisher: Elsevier
ISBN: 008087262X
Category : Mathematics
Languages : en
Pages : 431

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Book Description
This third volume of the monograph examines potential theory. The first chapter develops potential theory with respect to a single kernel (or discrete time semigroup). All the essential ideas of the theory are presented: excessive functions, reductions, sweeping, maximum principle. The second chapter begins with a study of the notion of reduction in the most general situation possible - the ``gambling house'' of Dubins and Savage. The beautiful results presented have never been made accessible to a wide public. These are then connected with the theory of sweeping with respect to a cone of continuous functions, and the integral representation in compact convex sets. The third chapter presents new or little-known results, with the aim of illustrating the effectiveness of capacitary methods in the most varied fields. The last two chapters are concerned with the theory of resolvents.The fourth and last part of the English edition will be devoted to the theory of Markov processes.

Author: Glenn Shafer
Publisher: John Wiley & Sons
ISBN: 1118548027
Category : Business & Economics
Languages : en
Pages : 554

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Book Description
Game-theoretic probability and finance come of age Glenn Shafer and Vladimir Vovk’s Probability and Finance, published in 2001, showed that perfect-information games can be used to define mathematical probability. Based on fifteen years of further research, Game-Theoretic Foundations for Probability and Finance presents a mature view of the foundational role game theory can play. Its account of probability theory opens the way to new methods of prediction and testing and makes many statistical methods more transparent and widely usable. Its contributions to finance theory include purely game-theoretic accounts of Ito’s stochastic calculus, the capital asset pricing model, the equity premium, and portfolio theory. Game-Theoretic Foundations for Probability and Finance is a book of research. It is also a teaching resource. Each chapter is supplemented with carefully designed exercises and notes relating the new theory to its historical context. Praise from early readers “Ever since Kolmogorov's Grundbegriffe, the standard mathematical treatment of probability theory has been measure-theoretic. In this ground-breaking work, Shafer and Vovk give a game-theoretic foundation instead. While being just as rigorous, the game-theoretic approach allows for vast and useful generalizations of classical measure-theoretic results, while also giving rise to new, radical ideas for prediction, statistics and mathematical finance without stochastic assumptions. The authors set out their theory in great detail, resulting in what is definitely one of the most important books on the foundations of probability to have appeared in the last few decades.” – Peter Grünwald, CWI and University of Leiden “Shafer and Vovk have thoroughly re-written their 2001 book on the game-theoretic foundations for probability and for finance. They have included an account of the tremendous growth that has occurred since, in the game-theoretic and pathwise approaches to stochastic analysis and in their applications to continuous-time finance. This new book will undoubtedly spur a better understanding of the foundations of these very important fields, and we should all be grateful to its authors.” – Ioannis Karatzas, Columbia University

Author: Jean-Paul Zolesio
Publisher: CRC Press
ISBN: 1482277689
Category : Mathematics
Languages : en
Pages : 417

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Book Description
Based on the Working Conference on Boundary Control and Boundary Variation held in Sophia-Antipolis, France, this work provides important examinations of shape optimization and boundary control of hyperbolic systems, including free boundary problems and stabilization. It offers a new approach to large and nonlinear variation of the boundary using g

Author: V.P. Khavin
Publisher: Springer Science & Business Media
ISBN: 3662063018
Category : Mathematics
Languages : en
Pages : 235

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Book Description
With the groundwork laid in the first volume (EMS 15) of the Commutative Harmonic Analysis subseries of the Encyclopaedia, the present volume takes up four advanced topics in the subject: Littlewood-Paley theory for singular integrals, exceptional sets, multiple Fourier series and multiple Fourier integrals.

Author: M. C. Delfour
Publisher: SIAM
ISBN: 0898719364
Category : Mathematics
Languages : en
Pages : 637

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Book Description
Presents the latest groundbreaking theoretical foundation to shape optimization in a form accessible to mathematicians, scientists and engineers.

Author: Library of Congress. Copyright Office
Publisher: Copyright Office, Library of Congress
ISBN:
Category : Copyright
Languages : en
Pages : 1862

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Author: Giuseppe Da Prato
Publisher: CRC Press
ISBN: 1482277654
Category : Mathematics
Languages : en
Pages : 296

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Book Description
This useful reference provides recent results as well as entirely new material on control problems for partial differential equations.

Author: Guy Bouchitte
Publisher: World Scientific
ISBN: 9814550825
Category :
Languages : en
Pages : 312

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Book Description
The aim of the workshop was to promote a better understanding of the connections between recent problems in Theoretical or Computational Mechanics (bounds in composites, phase transitions, microstructure of crystals, optimal design, nonlinear elasticity) and new mathematical tools in the Calculus of Variations (relaxation and Γ-convergence theory, Young and H-measures, compensated compactness and quasiconvexity).