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Differential equations, Partial --- Harmonic analysis --- Homogenization (Differential equations) --- Lie groups --- Asymptotic theory

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This book gives a quick introduction to the theory of foliations, Lie groupoids and Lie algebroids. An important feature is the emphasis on the interplay between these concepts: Lie groupoids form an indispensable tool to study the transverse structure of foliations as well as their noncommutative geometry, while the theory of foliations has immediate applications to the Lie theory of groupoids and their infinitesimal algebroids. The book starts with a detailed presentation of the main classical theorems in the theory of foliations then proceeds to Molino's theory, Lie groupoids, constructing the holonomy groupoid of a foliation and finally Lie algebroids. Among other things, the authors discuss to what extent Lie's theory for Lie groups and Lie algebras holds in the more general context of groupoids and algebroids. Based on the authors' extensive teaching experience, this book contains numerous examples and exercises making it ideal for graduate students and their instructors.

Foliations (Mathematics). --- Mathematics --- Physical Sciences & Mathematics --- Geometry --- Foliations (Mathematics) --- Lie groupoids. --- Groupoids --- Lie groups --- Foliated structures --- Differential topology

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Semisimple Lie groups. --- Groupes de Lie semi-simples --- Lie, Groupes de --- Traite d'analyse mathematique --- Groupes topologiques --- Groupes compacts --- Traite d'analyse mathematique --- Groupes topologiques --- Groupes compacts

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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)