an:01825536
Zbl 1013.28012
Kharazishvili, A. B.
Transformation groups and invariant measures. Set-theoretical aspects
EN
Singapore: World Scientific. viii, 260 p. (1998).
1998
b
28C10 03E15 28-01 37A15
invariant measure; quasiinvariant measure; transformation group
This book is an exposition of the classical theory of measures, defined on \(\sigma\)-algebras of spaces \(X\), that are invariant with respect to a transformation group of \(X\). Indeed, the book is based on graduate course lectures on the subject. Scattered throughout the book are a significant number of exercises for the student to test his understanding of the subject matter.
Topics covered in the book include standard facts concerning Lebesgue and Borel measures. The tenth and final chapter present the Mackey-Weil theorem providing a characterization of \(\sigma\)-finite quasiinvariant Borel meausures on standard groups. A group is said to be standard if it is a Borel subgroup of some Polish group.
Benjamin B.Wells jun.(Charlotte)