On Generators of Shy Sets in Polish Groups de Gogi Rauli Pantsulaia

On Generators of Shy Sets in Polish Groups

Gogi Rauli Pantsulaia

This book explores a number of new constructions of generators of shy sets (Mankiewicz generator, Preiss-Tiser generator, Baker generator, Kharazishvili generator, ordinary and standard Lebesgue measures, etc), which naturally generate classes of null sets playing an important role in studying the properties of a function space. It includes several interesting infinite-dimensional generalisations of some classical results (Cramer rule, Lioville theorem, etc) in terms of generators of shy sets.

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Cuprins

Introduction; Basic Concepts; Invariant Borel Measures in RN 21; On Partial Analogs of the Lebesgue Measure in Solovay Model; On generators of shy sets on Polish topological vector spaces; Liouville-type theorems for generators of shy sets in RN 75; On a certain partition of the abelian Polish group RN; On a certain problem of E. Szpilrajn for complete metric spaces; On left-invariant probability measures on general groups; On a certain question of P.Komjath; On ordinary & standard Lebesgue measures on R¥; On a standard product of an arbitrary family of s-finite Borel measures with domain in Polish spaces; Change of variable formula for the a-ordinary Lebesgue measure on RN; On a certain criterion of shyness for subsets in the product of unimodular Polish groups that are not compact; On a generalized Fourier µ-series in some infinite-dimensional Polish topological vector spaces; Invariant Extensions of Haar Measures; On ordinary & standard products of a countable family of measures & some of their applications; Index.