Selected Topics of Invariant Measures in Polish Groups

Gogi Pantsulaia (Autor)

Buch | Hardcover

233 Seiten

2014
Nova Science Publishers Inc (Verlag)
978-1-62948-831-8 (ISBN)

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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.

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 -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 -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. Erdoes Problem for Translation-Invariant Quasi-Finite Diffused Borel Measures in Polish Groups that are not Locally Compact; On a Certain Version of the Erdoes Problem Appendix; References; Index.

Verlagsort	New York
Sprache	englisch
Maße	180 x 260 mm
Gewicht	580 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
ISBN-10	1-62948-831-3 / 1629488313
ISBN-13	978-1-62948-831-8 / 9781629488318
Zustand	Neuware