Measures with Symmetry Properties

• Main Author: Schindler, Werner (Author, http://id.loc.gov/vocabulary/relators/aut)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2003.
• Edition: 1st ed. 2003.
• Series: Lecture Notes in Mathematics, 1808
• Subjects: Measure theory.; Topological groups.; Lie groups.; Numerical analysis.; Statistics .; Measure and Integration.; Topological Groups, Lie Groups.; Numerical Analysis.; Statistical Theory and Methods.

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 speci...

Table of Contents:

• 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.