Overview

This book explores a number of new applications of invariant quasi-finite diffused Borel measures in Polish groups for a solution of various problems stated by famous mathematicians (for example, Carmichael, Erdos, Fremlin, Darji and so on). By using natural Borel embeddings of an infinite-dimensional function space into the standard topological vector space of all real-valued sequences, (endowed with the Tychonoff topology) a new approach for the construction of different translation-invariant quasi-finite diffused Borel measures with suitable properties and for their applications in a solution of various partial differential equations in an entire vector space is proposed.

Full Product Details

Author:   Gogi Pantsulaia
Publisher:   Nova Science Publishers Inc
Imprint:   Nova Science Publishers Inc
Dimensions:   Width: 18.00cm , Height: 1.80cm , Length: 26.00cm
Weight:   0.580kg
ISBN:  

9781629488318

ISBN 10:   1629488313
Pages:   233
Publication Date:   01 March 2014
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Hardback
Publisher's Status:   Active
Availability:   Available To Order  
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Table of Contents

Preface; Introduction; On Ordinary & Standard Lebesgue Measures in R ; On Uniformly Distributed Sequences of an Increasing Family of Finite Sets in Infinite-Dimensional Rectangles; Change of Variable Formula for the alpha-Ordinary Lebesgue Measure in RN; On Existence & Uniqueness of Generators of Shy Sets in Polish Groups; On a Certain Criterion of Shyness for Subsets in the Product of Unimodular Polish Groups that are not Compact; On Ordinary & Standard Lebesgue Measures in Separable Banach Spaces; On a Standard Product of an Arbitrary Family of sigma-Finite Borel Measures with Domain in Polish Spaces; On Strict Standard & Strict Ordinary Products of Measures & Some of their Applications; On an Explicit Representation of a Particular Solution of the Non-Homogeneous Differential Equation of the Higher Order with Real Constant Coefficients; An Invariant Measure for the Non-Homogeneous Ordinary Differential Equation of Infinite Order with Real Constant Coefficients; Description of the Behaviour of von Foerster-Lasota Phase Motions in R in Terms of Ordinary & Standard Lebesgue Measures; On Uniformly Distributed Sequences on [- 1/2, 1/2]; An Expansion into an Infinite-Dimensional Multiple Trigonometric Series of a Square Integrable Function in R ; On Questions of U. Darji & D. Fremlin On a Certain Modification of P. Erdos Problem for Translation-Invariant Quasi-Finite Diffused Borel Measures in Polish Groups that are not Locally Compact; On a Certain Version of the Erdos Problem Appendix; References; Index.

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