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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.

Measure theory. --- Probability measures. --- Measure theory --- Probability measures --- Set functions --- Mathematical Theory --- Calculus --- Mathematics --- Physical Sciences & Mathematics --- Topological groups. --- Lie groups. --- Numerical analysis. --- Statistics . --- Measure and Integration. --- Topological Groups, Lie Groups. --- Numerical Analysis. --- Statistical Theory and Methods. --- Statistical analysis --- Statistical data --- Statistical methods --- Statistical science --- Econometrics --- Mathematical analysis --- Groups, Lie --- Lie algebras --- Symmetric spaces --- Topological groups --- Groups, Topological --- Continuous groups --- Lebesgue measure --- Measurable sets --- Measure of a set --- Algebraic topology --- Integrals, Generalized --- Measure algebras --- Rings (Algebra)