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Author: A. B. Kharazishvili Publisher: World Scientific ISBN: 9810234929 Category : Mathematics Languages : en Pages : 270
Book Description
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: A. B. Kharazishvili Publisher: World Scientific ISBN: 9810234929 Category : Mathematics Languages : en Pages : 270
Book Description
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: Nail H. Ibragimov Publisher: Springer Science & Business Media ISBN: 9781402003394 Category : Science Languages : en Pages : 422
Book Description
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 Publisher: Springer Science & Business Media ISBN: 3642666930 Category : Mathematics Languages : en Pages : 387
Book Description
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: Alexander Kharazishvili Publisher: CRC Press ISBN: 1040014283 Category : Mathematics Languages : en Pages : 416
Book Description
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: A. B. Kharazishvili
Author: A. B. Kharazishvili
Author: Robert A. Wijsman
Author: Edward G. Effros
Author: Ole E Barndorff-Nielsen
Author: Gary Bernard Laison
Author: Nail H. Ibragimov
Author: Hidegorō Nakano
Author: I.E. Segal
Author: 
Author: Alexander Kharazishvili