Transformation Groups And Invariant Measures

Author : A B Kharazishvili
Publisher : World Scientific
Page : 268 pages
File Size : 41,5 Mb
Release : 1998-10-05
Category : Mathematics
ISBN : 9789814518222

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Transformation Groups and Invariant Measures by A B Kharazishvili Pdf

This book is devoted to some topics of the general theory of invariant and quasi-invariant measures. Such measures are usually defined on various σ-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. Contents:Some Properties of Transformation GroupsQuasiinvariant and Invariant MeasuresSome Examples and ConstructionsNonmeasurable Sets with Respect to Quasiinvariant and Invariant MeasuresSmall Sets with Respect to Quasiinvariant MeasuresAlmost Invariant SetsSome Invariant σ-Ideals and σ-AlgebrasDensity Points and Invariant Extensions of Lebesgue MeasureThe Uniqueness of Lebesgue and Borel MeasuresQuasiinvariant Borel Measures on Standard Groups Readership: Pure mathematicians. Keywords:Transformation Group;Invariant Measure;Quasi-Invariant Measure;Absolutely Negligible Set;Absolutely Nonmeasurable Set;Extension of Measure;Haar Measure;Lebesgue Measure;Uniqueness Property for Measures;Steinhaus Property;Metrical Transitivity;Standard Group;Measurable Cardinal

Author : A. B. Kharazishvili
Publisher : World Scientific
Page : 270 pages
File Size : 54,6 Mb
Release : 1998
Category : Mathematics
ISBN : 9789810234928

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Transformation Groups and Invariant Measures by A. B. Kharazishvili Pdf

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.

Author : Robert A. Wijsman
Publisher : IMS
Page : 264 pages
File Size : 46,5 Mb
Release : 1990
Category : Mathematics
ISBN : 0940600196

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Invariant Measures on Groups and Their Use in Statistics by Robert A. Wijsman Pdf

Author : Edward G. Effros,Frank Hahn,Frank John Hahn
Publisher : American Mathematical Soc.
Page : 92 pages
File Size : 54,6 Mb
Release : 1967
Category : Algebras, Linear
ISBN : 9780821812754

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Locally Compact Transformation Groups and C^*-Algebras by Edward G. Effros,Frank Hahn,Frank John Hahn Pdf

Author : Doug Pickrell
Publisher : American Mathematical Soc.
Page : 125 pages
File Size : 46,8 Mb
Release : 2000
Category : Mathematics
ISBN : 9780821820681

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Invariant Measures for Unitary Groups Associated to Kac-Moody Lie Algebras by Doug Pickrell Pdf

The main purpose of this paper is to prove the existence, and in some cases the uniqueness, of unitarily invariant measures on formal completions of groups associated to affine Kac-Moody algebras, and associated homogeneous spaces. The basic invariant measure is a natural generalization of Haar measure for a simply connected compact Lie group, and its projection to flag spaces is a generalization of the normalized invariant volume element. The other ``invariant measures'' are actually measures having values in line bundles over these spaces; these bundle-valued measures heuristically arise from coupling the basic invariant measure to Hermitian structures on associated line bundles, but in this infinite dimensional setting they are generally singular with respect to the basic invariant measure.

Author : Ole E Barndorff-Nielsen,Preben Blaesild,Poul S. Eriksen
Publisher : Springer Science & Business Media
Page : 154 pages
File Size : 47,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461236825

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Decomposition and Invariance of Measures, and Statistical Transformation Models by Ole E Barndorff-Nielsen,Preben Blaesild,Poul S. Eriksen Pdf

Author : Alex Lubotzky
Publisher : Springer Science & Business Media
Page : 201 pages
File Size : 47,7 Mb
Release : 2010-02-17
Category : Mathematics
ISBN : 9783034603324

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Discrete Groups, Expanding Graphs and Invariant Measures by Alex Lubotzky Pdf

In the last ?fteen years two seemingly unrelated problems, one in computer science and the other in measure theory, were solved by amazingly similar techniques from representation theory and from analytic number theory. One problem is the - plicit construction of expanding graphs («expanders»). These are highly connected sparse graphs whose existence can be easily demonstrated but whose explicit c- struction turns out to be a dif?cult task. Since expanders serve as basic building blocks for various distributed networks, an explicit construction is highly des- able. The other problem is one posed by Ruziewicz about seventy years ago and studied by Banach [Ba]. It asks whether the Lebesgue measure is the only ?nitely additive measure of total measure one, de?ned on the Lebesgue subsets of the n-dimensional sphere and invariant under all rotations. The two problems seem, at ?rst glance, totally unrelated. It is therefore so- what surprising that both problems were solved using similar methods: initially, Kazhdan’s property (T) from representation theory of semi-simple Lie groups was applied in both cases to achieve partial results, and later on, both problems were solved using the (proved) Ramanujan conjecture from the theory of automorphic forms. The fact that representation theory and automorphic forms have anything to do with these problems is a surprise and a hint as well that the two questions are strongly related.

Author : Alexander Lubotzky
Publisher : Unknown
Page : 173 pages
File Size : 40,6 Mb
Release : 1989
Category : Electronic
ISBN : OCLC:716151995

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Discrete Groups, Expanding Graphs and Invariant Measures by Alexander Lubotzky Pdf

Author : Nail H. Ibragimov
Publisher : Springer Science & Business Media
Page : 422 pages
File Size : 44,5 Mb
Release : 2001-11-30
Category : Science
ISBN : 1402003390

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Transformation Groups Applied to Mathematical Physics by Nail H. Ibragimov Pdf

Approach your problems from the right It isn't that they can't see the solution. end and begin with the answers. Then It is that they can't see the problem. one day, perhaps you will find the final question. G.K. Chesterton. The Scandal of Father Brown 'The Point of a Pin'. 'The Hermit Clad in Crane Feathers' in R.van Gulik's The Chinese Maze Murders. Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non-trivially) in - gional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in pack ing and covering theory; quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces. And in addition to this there are such new emerging subdisciplines as "completely integrable systems", "chaos, synergetics and large-scale order", which are almost impossible to fit into the existing classification schemes. They draw upon widely different sections of mathematics.

Author : I.E. Segal,R.A. Kunze
Publisher : Springer Science & Business Media
Page : 387 pages
File Size : 42,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642666933

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Integrals and Operators by I.E. Segal,R.A. Kunze Pdf

TO THE SECOND EDITION Since publication of the First Edition several excellent treatments of advanced topics in analysis have appeared. However, the concentration and penetration of these treatises naturally require much in the way of technical preliminaries and new terminology and notation. There consequently remains a need for an introduction to some of these topics which would mesh with the material of the First Edition. Such an introduction could serve to exemplify the material further, while using it to shorten and simplify its presentation. It seemed particularly important as well as practical to treat briefly but cogently some of the central parts of operator algebra and higher operator theory, as these are presently represented in book form only with a degree of specialization rather beyond the immediate needs or interests of many readers. Semigroup and perturbation theory provide connections with the theory of partial differential equations. C*-algebras are important in har monic analysis and the mathematical foundations of quantum mechanics. W*-algebras (or von Neumann rings) provide an approach to the theory of multiplicity of the spectrum and some simple but key elements of the gram mar of analysis, of use in group representation theory and elsewhere. The v vi Preface to the Second Edition theory of the trace for operators on Hilbert space is both important in itself and a natural extension of earlier integration-theoretic ideas.

Author : T. Tom Dieck
Publisher : Springer
Page : 317 pages
File Size : 47,7 Mb
Release : 2006-11-15
Category : Mathematics
ISBN : 9783540385172

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Transformation Groups and Representation Theory by T. Tom Dieck Pdf

Author : Anonim
Publisher : Academic Press
Page : 424 pages
File Size : 47,7 Mb
Release : 1972-10-16
Category : Mathematics
ISBN : 0080873634

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Measure and Integration Theory on Infinite-Dimensional Spaces by Anonim Pdf

Measure and Integration Theory on Infinite-Dimensional Spaces

Author : Alexander Kharazishvili
Publisher : CRC Press
Page : 416 pages
File Size : 51,5 Mb
Release : 2024-05-15
Category : Mathematics
ISBN : 9781040014288

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Introduction to Combinatorial Methods in Geometry by Alexander Kharazishvili Pdf

This book offers an introduction to some combinatorial (also, set-theoretical) approaches and methods in geometry of the Euclidean space Rm. The topics discussed in the manuscript are due to the field of combinatorial and convex geometry. The author’s primary intention is to discuss those themes of Euclidean geometry which might be of interest to a sufficiently wide audience of potential readers. Accordingly, the material is explained in a simple and elementary form completely accessible to the college and university students. At the same time, the author reveals profound interactions between various facts and statements from different areas of mathematics: the theory of convex sets, finite and infinite combinatorics, graph theory, measure theory, classical number theory, etc. All chapters (and also the five Appendices) end with a number of exercises. These provide the reader with some additional information about topics considered in the main text of this book. Naturally, the exercises vary in their difficulty. Among them there are almost trivial, standard, nontrivial, rather difficult, and difficult. As a rule, more difficult exercises are marked by asterisks and are provided with necessary hints. The material presented is based on the lecture course given by the author. The choice of material serves to demonstrate the unity of mathematics and variety of unexpected interrelations between distinct mathematical branches.

Author : Michiel Hazewinkel
Publisher : Springer Science & Business Media
Page : 555 pages
File Size : 43,8 Mb
Release : 2013-12-01
Category : Mathematics
ISBN : 9789400959910

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Encyclopaedia of Mathematics by Michiel Hazewinkel Pdf

This ENCYCLOPAEDIA OF MATHEMATICS aims to be a reference work for all parts of mathe matics. It is a translation with updates and editorial comments of the Soviet Mathematical Encyclopaedia published by 'Soviet Encyclopaedia Publishing House' in five volumes in 1977-1985. The annotated translation consists of ten volumes including a special index volume. There are three kinds of articles in this ENCYCLOPAEDIA. First of all there are survey-type articles dealing with the various main directions in mathematics (where a rather fine subdivi sion has been used). The main requirement for these articles has been that they should give a reasonably complete up-to-date account of the current state of affairs in these areas and that they should be maximally accessible. On the whole, these articles should be understandable to mathematics students in their first specialization years, to graduates from other mathematical areas and, depending on the specific subject, to specialists in other domains of science, en gineers and teachers of mathematics. These articles treat their material at a fairly general level and aim to give an idea of the kind of problems, techniques and concepts involved in the area in question. They also contain background and motivation rather than precise statements of precise theorems with detailed definitions and technical details on how to carry out proofs and constructions. The second kind of article, of medium length, contains more detailed concrete problems, results and techniques.

Author : Nihon Sūgakkai
Publisher : MIT Press
Page : 1180 pages
File Size : 42,9 Mb
Release : 1993
Category : Mathematics
ISBN : 0262590204

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Encyclopedic Dictionary of Mathematics by Nihon Sūgakkai Pdf

V.1. A.N. v.2. O.Z. Apendices and indexes.