Measures with Symmetry Properties

Measures with Symmetry Properties

by Werner Schindler


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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.

Product Details

ISBN-13: 9783540002352
Publisher: Springer Berlin Heidelberg
Publication date: 02/12/2003
Series: Lecture Notes in Mathematics , #1808
Edition description: 2003
Pages: 174
Product dimensions: 6.10(w) x 9.25(h) x 0.36(d)

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.

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