Measures with symmetry properties
type: Item
instance of: scholarly article
title: Measures with symmetry properties
zbMATH Open document ID: 1065.28007
published in: Lecture Notes in Mathematics
publication date: 2003-01-27T00:00:00Z
review text: The symmetry properties of Haar measures and invariant measures on homogeneous spaces have been exploited in various branches of mathematics in the past. The title `Measures with symmetry properties' of the book indicates, that this book treats measures which are invariant under group actions, i.e., more precisely, it allows measures which in general have a lower degree of symmetry than Haar measures or invariant measures on homogeneous spaces. Clearly such measures are no longer uniquely determined, but this weakening of the symmetry properties combined with a more general framework opens an amazingly wide range of applications, which is peculiar to this work. On the other hand it affords harder mathematical work going deeper as before. It should be said at once that the latter does not mean that this book addresses only to pure or applied mathematicians, but also to computer scientists, statisticians, and engineers. For this reason great care is given to make the book easy accessible to readers from a great variety of different backgrounds in keeping the mathematical prerequisites to a minimum and by making the exposition essentially self-contained. For a better understanding basic definitions and theorems are always illustrated by simple examples familiar from calculus. The mathematical core of this book is condensed in one single chapter which can be skipped at a first reading by those interested only in applications. As the main part the chapter on applications occupies about two third of the whole treatise and considers problems on integration, stochastic simulation, and statistics. The examples range from computational geometry, Grassmannian manifolds, compact connected Lie groups, applied mathematics, computer aided graphic design to coding theory. All these topics are discussed in great detail and for an easy access all mathematical tools are summarized at the beginning of the chapter for better reference. Great care is given to illustrate how the fundament…
Mathematics Subject Classification ID: 28C10
Mathematics Subject Classification ID: 43A05
Mathematics Subject Classification ID: 43A85
Mathematics Subject Classification ID: 28-01
zbMATH DE Number: 1859092
zbMATH Keywords: invariant measure
zbMATH Keywords: Haar measure
zbMATH Keywords: pseudorandom variable
zbMATH Keywords: efficiently generated algorithms
author: Werner Schindler
reviewed by: Werner Strauß
MaRDI profile type: Publication
full work available at URL: b80163
OpenAlex ID: W4210873660
DOI: 10.1007/B80163
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description: scientific article; zbMATH DE number 1859092