Measures with Symmetry Properties

Werner Schindler

176 pages, parution le 18/02/2003

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Résumé

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.

Contents

Introduction

Main Theorems

Definitions and Preparatory Lemmata
Definition of Property (*) and Its Implications (Main Results)
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

L'auteur - Werner Schindler

Bundesamt für Sicherheit in der Informationstechnik, Bonn, Germany

Caractéristiques techniques

	PAPIER
Éditeur(s)	Springer
Auteur(s)	Werner Schindler
Parution	18/02/2003
Nb. de pages	176
Format	15,5 x 23,5
Couverture	Broché
Poids	274g
Intérieur	Noir et Blanc
EAN13	9783540002352