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Topological Measures And Weighted Radon Measures
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Book Synopsis Topological Measures and Weighted Radon Measures by : Domenico P. L. Castrigiano
Download or read book Topological Measures and Weighted Radon Measures written by Domenico P. L. Castrigiano and published by Alpha Science International, Limited. This book was released on 2008 with total page 284 pages. Available in PDF, EPUB and Kindle. Book excerpt: Due to the close interplay of measure and topology, topological measure theory is a particularly intriguing part of general measure theory. This book introduces chapters on abstract measure theory.
Book Synopsis Transformation Groups and Invariant Measures by : A. B. Kharazishvili
Download or read book Transformation Groups and Invariant Measures written by A. B. Kharazishvili and published by World Scientific. This book was released on 1998 with total page 270 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to some topics of the general theory of invariant and quasi-invariant measures. Such measures are usually defined on various sigma-algebras of subsets of spaces equipped with transformation groups, and there are close relationships between purely algebraic properties of these groups and the corresponding properties of invariant (quasi-invariant) measures. The main goal of the book is to investigate several aspects of those relationships (primarily from the set-theoretical point of view). Also of interest are the properties of some natural classes of sets, important from the viewpoint of the theory of invariant (quasi-invariant) measures.
Book Synopsis Measure-valued differentiations for finite products of measures by : Haralambie Leahu
Download or read book Measure-valued differentiations for finite products of measures written by Haralambie Leahu and published by Rozenberg Publishers. This book was released on 2008 with total page 160 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Measure Theory written by D. H. Fremlin and published by Torres Fremlin. This book was released on 2000 with total page 967 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Handbook of Measure Theory by : E. Pap
Download or read book Handbook of Measure Theory written by E. Pap and published by Elsevier. This book was released on 2002-10-31 with total page 1633 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main goal of this Handbook isto survey measure theory with its many different branches and itsrelations with other areas of mathematics. Mostly aggregating many classical branches of measure theory the aim of the Handbook is also to cover new fields, approaches and applications whichsupport the idea of "measure" in a wider sense, e.g. the ninth part of the Handbook. Although chapters are written of surveys in the variousareas they contain many special topics and challengingproblems valuable for experts and rich sources of inspiration.Mathematicians from other areas as well as physicists, computerscientists, engineers and econometrists will find useful results andpowerful methods for their research. The reader may find in theHandbook many close relations to other mathematical areas: realanalysis, probability theory, statistics, ergodic theory,functional analysis, potential theory, topology, set theory,geometry, differential equations, optimization, variationalanalysis, decision making and others. The Handbook is a richsource of relevant references to articles, books and lecturenotes and it contains for the reader's convenience an extensivesubject and author index.
Book Synopsis Young Measures on Topological Spaces by : Charles Castaing
Download or read book Young Measures on Topological Spaces written by Charles Castaing and published by Springer Science & Business Media. This book was released on 2004-07-14 with total page 327 pages. Available in PDF, EPUB and Kindle. Book excerpt: Young measures are now a widely used tool in the Calculus of Variations, in Control Theory, in Probability Theory and other fields. They are known under different names such as "relaxed controls", "fuzzy random variables" and many other names. This monograph provides a unified presentation of the theory, along with new results and applications in various fields. It can serve as a reference on the subject. Young measures are presented in a general setting which includes finite and for the first time infinite dimensional spaces: the fields of applications of Young measures (Control Theory, Calculus of Variations, Probability Theory...) are often concerned with problems in infinite dimensional settings. The theory of Young measures is now well understood in a finite dimensional setting, but open problems remain in the infinite dimensional case. We provide several new results in the general frame, which are new even in the finite dimensional setting, such as characterizations of convergence in measure of Young measures (Chapter 3) and compactness criteria (Chapter 4).These results are established under a different form (and with fewer details and developments) in recent papers by the same authors. We also provide new applications to Visintin and Reshetnyak type theorems (Chapters 6 and 8), existence of solutions to differential inclusions (Chapter 7), dynamical programming (Chapter 8) and the Central Limit Theorem in locally convex spaces (Chapter 9).
Book Synopsis Handbook of Set-Theoretic Topology by : K. Kunen
Download or read book Handbook of Set-Theoretic Topology written by K. Kunen and published by Elsevier. This book was released on 2014-06-28 with total page 1282 pages. Available in PDF, EPUB and Kindle. Book excerpt: This Handbook is an introduction to set-theoretic topology for students in the field and for researchers in other areas for whom results in set-theoretic topology may be relevant. The aim of the editors has been to make it as self-contained as possible without repeating material which can easily be found in standard texts. The Handbook contains detailed proofs of core results, and references to the literature for peripheral results where space was insufficient. Included are many open problems of current interest.In general, the articles may be read in any order. In a few cases they occur in pairs, with the first one giving an elementary treatment of a subject and the second one more advanced results. These pairs are: Hodel and Juhász on cardinal functions; Roitman and Abraham-Todorčević on S- and L-spaces; Weiss and Baumgartner on versions of Martin's axiom; and Vaughan and Stephenson on compactness properties.
Book Synopsis Harmonic Analysis of Probability Measures on Hypergroups by : Walter R. Bloom
Download or read book Harmonic Analysis of Probability Measures on Hypergroups written by Walter R. Bloom and published by Walter de Gruyter. This book was released on 2011-04-20 with total page 609 pages. Available in PDF, EPUB and Kindle. Book excerpt: The series is devoted to the publication of monographs and high-level textbooks in mathematics, mathematical methods and their applications. Apart from covering important areas of current interest, a major aim is to make topics of an interdisciplinary nature accessible to the non-specialist. The works in this series are addressed to advanced students and researchers in mathematics and theoretical physics. In addition, it can serve as a guide for lectures and seminars on a graduate level. The series de Gruyter Studies in Mathematics was founded ca. 30 years ago by the late Professor Heinz Bauer and Professor Peter Gabriel with the aim to establish a series of monographs and textbooks of high standard, written by scholars with an international reputation presenting current fields of research in pure and applied mathematics. While the editorial board of the Studies has changed with the years, the aspirations of the Studies are unchanged. In times of rapid growth of mathematical knowledge carefully written monographs and textbooks written by experts are needed more than ever, not least to pave the way for the next generation of mathematicians. In this sense the editorial board and the publisher of the Studies are devoted to continue the Studies as a service to the mathematical community. Please submit any book proposals to Niels Jacob.
Author :Alexander Kharazishvili Publisher :Springer Science & Business Media ISBN 13 :9491216368 Total Pages :466 pages Book Rating :4.4/5 (912 download)
Book Synopsis TOPICS IN MEASURE THEORY AND REAL ANALYSIS by : Alexander Kharazishvili
Download or read book TOPICS IN MEASURE THEORY AND REAL ANALYSIS written by Alexander Kharazishvili and published by Springer Science & Business Media. This book was released on 2009-11-01 with total page 466 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book highlights various topics on measure theory and vividly demonstrates that the different questions of this theory are closely connected with the central measure extension problem. Several important aspects of the measure extension problem are considered separately: set-theoretical, topological and algebraic. Also, various combinations (e.g., algebraic-topological) of these aspects are discussed by stressing their specific features. Several new methods are presented for solving the above mentioned problem in concrete situations. In particular, the following new results are obtained: the measure extension problem is completely solved for invariant or quasi-invariant measures on solvable uncountable groups; non-separable extensions of invariant measures are constructed by using their ergodic components; absolutely non-measurable additive functionals are constructed for certain classes of measures; the structure of algebraic sums of measure zero sets is investigated. The material presented in this book is essentially self-contained and is oriented towards a wide audience of mathematicians (including postgraduate students). New results and facts given in the book are based on (or closely connected with) traditional topics of set theory, measure theory and general topology such as: infinite combinatorics, Martin's Axiom and the Continuum Hypothesis, Luzin and Sierpinski sets, universal measure zero sets, theorems on the existence of measurable selectors, regularity properties of Borel measures on metric spaces, and so on. Essential information on these topics is also included in the text (primarily, in the form of Appendixes or Exercises), which enables potential readers to understand the proofs and follow the constructions in full details. This not only allows the book to be used as a monograph but also as a course of lectures for students whose interests lie in set theory, real analysis, measure theory and general topology.
Book Synopsis Set Theoretical Aspects of Real Analysis by : Alexander B. Kharazishvili
Download or read book Set Theoretical Aspects of Real Analysis written by Alexander B. Kharazishvili and published by CRC Press. This book was released on 2014-08-26 with total page 457 pages. Available in PDF, EPUB and Kindle. Book excerpt: Set Theoretical Aspects of Real Analysis is built around a number of questions in real analysis and classical measure theory, which are of a set theoretic flavor. Accessible to graduate students, and researchers the beginning of the book presents introductory topics on real analysis and Lebesgue measure theory. These topics highlight the boundary between fundamental concepts of measurability and nonmeasurability for point sets and functions. The remainder of the book deals with more specialized material on set theoretical real analysis. The book focuses on certain logical and set theoretical aspects of real analysis. It is expected that the first eleven chapters can be used in a course on Lebesque measure theory that highlights the fundamental concepts of measurability and non-measurability for point sets and functions. Provided in the book are problems of varying difficulty that range from simple observations to advanced results. Relatively difficult exercises are marked by asterisks and hints are included with additional explanation. Five appendices are included to supply additional background information that can be read alongside, before, or after the chapters. Dealing with classical concepts, the book highlights material not often found in analysis courses. It lays out, in a logical, systematic manner, the foundations of set theory providing a readable treatment accessible to graduate students and researchers.
Book Synopsis Groups and Analysis by : Katrin Tent
Download or read book Groups and Analysis written by Katrin Tent and published by Cambridge University Press. This book was released on 2008-10-16 with total page 327 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many areas of mathematics were deeply influenced or even founded by Hermann Weyl, including geometric foundations of manifolds and physics, topological groups, Lie groups and representation theory, harmonic analysis and analytic number theory as well as foundations of mathematics. In this volume, leading experts present his lasting influence on current mathematics, often connecting Weyl's theorems with cutting edge research in dynamical systems, invariant theory, and partial differential equations. In a broad and accessible presentation, survey chapters describe the historical development of each area alongside up-to-the-minute results, focussing on the mathematical roots evident within Weyl's work.
Book Synopsis Geometry and Analysis of Metric Spaces via Weighted Partitions by : Jun Kigami
Download or read book Geometry and Analysis of Metric Spaces via Weighted Partitions written by Jun Kigami and published by Springer Nature. This book was released on 2020-11-16 with total page 164 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of these lecture notes is to propose a systematic framework for geometry and analysis on metric spaces. The central notion is a partition (an iterated decomposition) of a compact metric space. Via a partition, a compact metric space is associated with an infinite graph whose boundary is the original space. Metrics and measures on the space are then studied from an integrated point of view as weights of the partition. In the course of the text: It is shown that a weight corresponds to a metric if and only if the associated weighted graph is Gromov hyperbolic. Various relations between metrics and measures such as bilipschitz equivalence, quasisymmetry, Ahlfors regularity, and the volume doubling property are translated to relations between weights. In particular, it is shown that the volume doubling property between a metric and a measure corresponds to a quasisymmetry between two metrics in the language of weights. The Ahlfors regular conformal dimension of a compact metric space is characterized as the critical index of p-energies associated with the partition and the weight function corresponding to the metric. These notes should interest researchers and PhD students working in conformal geometry, analysis on metric spaces, and related areas.
Book Synopsis Differentiable Measures and the Malliavin Calculus by : Vladimir Igorevich Bogachev
Download or read book Differentiable Measures and the Malliavin Calculus written by Vladimir Igorevich Bogachev and published by American Mathematical Soc.. This book was released on 2010-07-21 with total page 506 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides the reader with the principal concepts and results related to differential properties of measures on infinite dimensional spaces. In the finite dimensional case such properties are described in terms of densities of measures with respect to Lebesgue measure. In the infinite dimensional case new phenomena arise. For the first time a detailed account is given of the theory of differentiable measures, initiated by S. V. Fomin in the 1960s; since then the method has found many various important applications. Differentiable properties are described for diverse concrete classes of measures arising in applications, for example, Gaussian, convex, stable, Gibbsian, and for distributions of random processes. Sobolev classes for measures on finite and infinite dimensional spaces are discussed in detail. Finally, we present the main ideas and results of the Malliavin calculus--a powerful method to study smoothness properties of the distributions of nonlinear functionals on infinite dimensional spaces with measures. The target readership includes mathematicians and physicists whose research is related to measures on infinite dimensional spaces, distributions of random processes, and differential equations in infinite dimensional spaces. The book includes an extensive bibliography on the subject.
Book Synopsis Measure and Measurable Dynamics by : R. Daniel Mauldin
Download or read book Measure and Measurable Dynamics written by R. Daniel Mauldin and published by American Mathematical Soc.. This book was released on 1989 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: Dorothy Maharam Stone's contributions to operators and measure algebras has had a profound influence on this area of research. This volume contains the proceedings of the Conference on Measure and Measurable Dynamics, held in honor of Stone at the University of Rochester in September 1987.
Book Synopsis Differential Equations on Measures and Functional Spaces by : Vassili Kolokoltsov
Download or read book Differential Equations on Measures and Functional Spaces written by Vassili Kolokoltsov and published by Springer. This book was released on 2019-06-20 with total page 536 pages. Available in PDF, EPUB and Kindle. Book excerpt: This advanced book focuses on ordinary differential equations (ODEs) in Banach and more general locally convex spaces, most notably the ODEs on measures and various function spaces. It briefly discusses the fundamentals before moving on to the cutting edge research in linear and nonlinear partial and pseudo-differential equations, general kinetic equations and fractional evolutions. The level of generality chosen is suitable for the study of the most important nonlinear equations of mathematical physics, such as Boltzmann, Smoluchovskii, Vlasov, Landau-Fokker-Planck, Cahn-Hilliard, Hamilton-Jacobi-Bellman, nonlinear Schroedinger, McKean-Vlasov diffusions and their nonlocal extensions, mass-action-law kinetics from chemistry. It also covers nonlinear evolutions arising in evolutionary biology and mean-field games, optimization theory, epidemics and system biology, in general models of interacting particles or agents describing splitting and merging, collisions and breakage, mutations and the preferential-attachment growth on networks. The book is intended mainly for upper undergraduate and graduate students, but is also of use to researchers in differential equations and their applications. It particularly highlights the interconnections between various topics revealing where and how a particular result is used in other chapters or may be used in other contexts, and also clarifies the links between the languages of pseudo-differential operators, generalized functions, operator theory, abstract linear spaces, fractional calculus and path integrals.
Book Synopsis Mathematical Concepts by : Jürgen Jost
Download or read book Mathematical Concepts written by Jürgen Jost and published by Springer. This book was released on 2015-09-10 with total page 315 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main intention of this book is to describe and develop the conceptual, structural and abstract thinking of mathematics. Specific mathematical structures are used to illustrate the conceptual approach; providing a deeper insight into mutual relationships and abstract common features. These ideas are carefully motivated, explained and illustrated by examples so that many of the more technical proofs can be omitted. The book can therefore be used: · simply as an overview of the panorama of mathematical structures and the relations between them, to be supplemented by more detailed texts whenever you want to acquire a working knowledge of some structure · by itself as a first introduction to abstract mathematics · together with existing textbooks, to put their results into a more general perspective · to gain a new and hopefully deeper perspective after having studied such textbooks Mathematical Concepts has a broader scope and is less detailed than standard mathematical textbooks so that the reader can readily grasp the essential concepts and ideas for individual needs. It will be suitable for advanced mathematicians, postgraduate students and for scientists from other fields with some background in formal reasoning.
Book Synopsis Saks Spaces and Applications to Functional Analysis by : J.B. Cooper
Download or read book Saks Spaces and Applications to Functional Analysis written by J.B. Cooper and published by Elsevier. This book was released on 2011-08-18 with total page 383 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first edition of this monograph appeared in 1978. In view of the progress made in the intervening years, the original text has been revised, several new sections have been added and the list of references has been updated. The book presents a systematic treatment of the theory of Saks Spaces, i.e. vector space with a norm and related, subsidiary locally convex topology. Applications are given to space of bounded, continuous functions, to measure theory, vector measures, spaces of bounded measurable functions, spaces of bounded analytic functions, and to W*-algebras.
