Invariant And Quasiinvariant Measures In Infinite Dimensional Topological Vector Spaces

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Invariant And Quasiinvariant Measures In Infinite Dimensional Topological Vector Spaces

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Author : Gogi Pantsulaia
language : en
Publisher:
Release Date : 2007

Invariant And Quasiinvariant Measures In Infinite Dimensional Topological Vector Spaces written by Gogi Pantsulaia and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Mathematics categories.

This monograph deals with certain aspects of the general theory of systems. The author develops the ergodic theory, which is the theory of quaslinvariant and invariant measures in such infinite-dimensional vector spaces which appear as models of various (physical, economic, genetic, linguistic, social, etc.) processes. The methods of ergodic theory are successful as applied to study properties of such systems. A foundation for ergodic theory was stimulated by the necessity of a consideration of statistic mechanic problems and was directly connected with the works of G. Birkhoff, Kryloff and Bogoliuboff, E. Hoph and other famous mathematicians.

Measures On Infinite Dimensional Spaces

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Author : Yasuo Yamasaki
language : en
Publisher: World Scientific
Release Date : 1985

Measures On Infinite Dimensional Spaces written by Yasuo Yamasaki and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1985 with Science categories.

This book is based on lectures given at Yale and Kyoto Universities and provides a self-contained detailed exposition of the following subjects: 1) The construction of infinite dimensional measures, 2) Invariance and quasi-invariance of measures under translations. This book furnishes an important tool for the analysis of physical systems with infinite degrees of freedom (such as field theory, statistical physics and field dynamics) by providing material on the foundations of these problems.

Measure And Integration Theory On Infinite Dimensional Spaces

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Author :
language : en
Publisher: Academic Press
Release Date : 1972-10-16

Measure And Integration Theory On Infinite Dimensional Spaces written by and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1972-10-16 with Mathematics categories.

Measure and Integration Theory on Infinite-Dimensional Spaces

Transformation Groups And Invariant Measures

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Author : A. B. Kharazishvili
language : en
Publisher: World Scientific
Release Date : 1998

Transformation Groups And Invariant Measures written by A. B. Kharazishvili and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with Mathematics categories.

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.

Functional Analysis And The Feynman Operator Calculus

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Author : Tepper Gill
language : en
Publisher: Springer
Release Date : 2016-03-30

Functional Analysis And The Feynman Operator Calculus written by Tepper Gill and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-03-30 with Mathematics categories.

This book provides the mathematical foundations for Feynman's operator calculus and for the Feynman path integral formulation of quantum mechanics as a natural extension of analysis and functional analysis to the infinite-dimensional setting. In one application, the results are used to prove the last two remaining conjectures of Freeman Dyson for quantum electrodynamics. In another application, the results are used to unify methods and weaken domain requirements for non-autonomous evolution equations. Other applications include a general theory of Lebesgue measure on Banach spaces with a Schauder basis and a new approach to the structure theory of operators on uniformly convex Banach spaces. This book is intended for advanced graduate students and researchers.

Semitopological Vector Spaces

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Author : Mark Burgin
language : en
Publisher: CRC Press
Release Date : 2017-06-26

Semitopological Vector Spaces written by Mark Burgin and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-06-26 with Mathematics categories.

This new volume shows how it is possible to further develop and essentially extend the theory of operators in infinite-dimensional vector spaces, which plays an important role in mathematics, physics, information theory, and control theory. The book describes new mathematical structures, such as hypernorms, hyperseminorms, hypermetrics, semitopological vector spaces, hypernormed vector spaces, and hyperseminormed vector spaces. It develops mathematical tools for the further development of functional analysis and broadening of its applications. Exploration of semitopological vector spaces, hypernormed vector spaces, hyperseminormed vector spaces, and hypermetric vector spaces is the main topic of this book. A new direction in functional analysis, called quantum functional analysis, has been developed based on polinormed and multinormed vector spaces and linear algebras. At the same time, normed vector spaces and topological vector spaces play an important role in physics and in control theory. To make this book comprehendible for the reader and more suitable for students with some basic knowledge in mathematics, denotations and definitions of the main mathematical concepts and structures used in the book are included in the appendix, making the book useful for enhancing traditional courses of calculus for undergraduates, as well as for separate courses for graduate students. The material of Semitopological Vector Spaces: Hypernorms, Hyperseminorms and Operators is closely related to what is taught at colleges and universities. It is possible to use a definite number of statements from the book as exercises for students because their proofs are not given in the book but left for the reader.

Geometric Aspects Of Probability Theory And Mathematical Statistics

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Author : V.V. Buldygin
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29

Geometric Aspects Of Probability Theory And Mathematical Statistics written by V.V. Buldygin and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-29 with Mathematics categories.

It is well known that contemporary mathematics includes many disci plines. Among them the most important are: set theory, algebra, topology, geometry, functional analysis, probability theory, the theory of differential equations and some others. Furthermore, every mathematical discipline consists of several large sections in which specific problems are investigated and the corresponding technique is developed. For example, in general topology we have the following extensive chap ters: the theory of compact extensions of topological spaces, the theory of continuous mappings, cardinal-valued characteristics of topological spaces, the theory of set-valued (multi-valued) mappings, etc. Modern algebra is featured by the following domains: linear algebra, group theory, the theory of rings, universal algebras, lattice theory, category theory, and so on. Concerning modern probability theory, we can easily see that the clas sification of its domains is much more extensive: measure theory on ab stract spaces, Borel and cylindrical measures in infinite-dimensional vector spaces, classical limit theorems, ergodic theory, general stochastic processes, Markov processes, stochastical equations, mathematical statistics, informa tion theory and many others.

Topics In Measure Theory And Real Analysis

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Author : Alexander Kharazishvili
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-11-01

Topics In Measure Theory And Real Analysis written by Alexander Kharazishvili and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-11-01 with Mathematics categories.

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.

Measures On Infinite Dimensional Spaces

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Author : Yasuo Yamasaki
language : en
Publisher: World Scientific
Release Date : 1985-07-01

Measures On Infinite Dimensional Spaces written by Yasuo Yamasaki and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1985-07-01 with Mathematics categories.

This book is based on lectures given at Yale and Kyoto Universities and provides a self-contained detailed exposition of the following subjects: 1) The construction of infinite dimensional measures, 2) Invariance and quasi-invariance of measures under translations. This book furnishes an important tool for the analysis of physical systems with infinite degrees of freedom (such as field theory, statistical physics and field dynamics) by providing material on the foundations of these problems.

Applications Of Measure Theory To Statistics

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Author : Gogi Pantsulaia
language : en
Publisher: Springer
Release Date : 2016-12-22

Applications Of Measure Theory To Statistics written by Gogi Pantsulaia and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-12-22 with Mathematics categories.

This book aims to put strong reasonable mathematical senses in notions of objectivity and subjectivity for consistent estimations in a Polish group by using the concept of Haar null sets in the corresponding group. This new approach – naturally dividing the class of all consistent estimates of an unknown parameter in a Polish group into disjoint classes of subjective and objective estimates – helps the reader to clarify some conjectures arising in the criticism of null hypothesis significance testing. The book also acquaints readers with the theory of infinite-dimensional Monte Carlo integration recently developed for estimation of the value of infinite-dimensional Riemann integrals over infinite-dimensional rectangles. The book is addressed both to graduate students and to researchers active in the fields of analysis, measure theory, and mathematical statistics.