Author	Schindler, Werner. author
Title	Measures with Symmetry Properties [electronic resource] / by Werner Schindler
Imprint	Berlin, Heidelberg : Springer Berlin Heidelberg, 2003
Connect to	http://dx.doi.org/10.1007/b80163
Descript	X, 174 p. online resource

Symmetries and invariance principles play an important role in various branches of mathematics. This book deals with measures having weak symmetry properties. Even mild conditions ensure that all invariant Borel measures on a second countable locally compact space can be expressed as images of specific product measures under a fixed mapping. The results derived in this book are interesting for their own and, moreover, a number of carefully investigated examples underline and illustrate their usefulness and applicability for integration problems, stochastic simulations and statistical applications

Introduction, Main Theorems: Definitions and Preparatory Lemmata; Definition of Property (*) and Its Implications (Main Theorems); Supplementary Expositions and an Alternate Existence Proof -- Significance, Applicability and Advantages -- Applications: Central Definitions, Theorems and Facts; Equidistribution on the Grassmannian Manifold and Chirotopes; Conjugation-invariant Probability Measures on Compact Connected Lie Groups; Conjugation-invariant Probability Measures on SO(n); Conjugation-invariant Probability Measures on SO(3); The Theorem of Iwasawa and Invariant Measures on Lie Groups; QR-Decomposition on GL(n); Polar Decomposition on GL(n); O(n)-invariant Borel Measures on Pos(n); Biinvariant Borel Measures on GL(n); Symmetries on Finite Spaces -- References -- Glossary -- Index

1. Mathematics
2. Topological groups
3. Lie groups
4. Measure theory
5. Numerical analysis
6. Statistics
7. Mathematics
8. Measure and Integration
9. Topological Groups
10. Lie Groups
11. Numerical Analysis
12. Statistical Theory and Methods