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TRANSFORMATION GROUPS AND INVARIANT MEASURES
Set-Theoretical Aspects
by A B Kharazishvili (Tbilisi State University, Republic of Georgia)
This book is devoted to some topics of the general theory of invariant and quasi-invariant measures. Such measures are usually defined on various s-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.
Contents:
- Some Properties of Transformation Groups
- Quasiinvariant and
Invariant Measures
- Some Examples and Constructions
- Nonmeasurable Sets with Respect to Quasiinvariant and Invariant Measures
- Small Sets with Respect to Quasiinvariant Measures
- Almost Invariant Sets
- Some Invariant s-Ideals and s-Algebras
- Density Points and Invariant Extensions of Lebesgue Measure
- The Uniqueness of Lebesgue and Borel Measures
- Quasiinvariant Borel Measures on Standard Groups
Readership: Pure mathematicians.
| 268pp |
Pub. date: Oct 1998 |
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