Measures with Symmetry Properties

• 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.

From the reviews: "This book treats measures which are invariant under group actions ... . great care is given to make the book easily 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." (Werner Strauss, Zentralblatt MATH, Vol. 1065, 2005)