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This book gives a straightforward introduction to the field as it is nowadays required in many branches of analysis and especially in probability theory. The first three chapters (Measure Theory, Integration Theory, Product Measures) basically follow the clear and approved exposition given in the author's earlier book on ""Probability Theory and Measure Theory"". Special emphasis is laid on a complete discussion of the transformation of measures and integration with respect to the product measure, convergence theorems, parameter depending integrals, as well as the Radon-Nikodym theorem.

Measure theory. --- Integrals, Generalized. --- Calculus, Integral --- Lebesgue measure --- Measurable sets --- Measure of a set --- Algebraic topology --- Integrals, Generalized --- Measure algebras --- Rings (Algebra)

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These notes provide a reasonably self-contained introductory survey of certain aspects of harmonic analysis on compact groups. The first part of the book seeks to give a brief account of integration theory on compact Hausdorff spaces. The second, larger part starts from the existence and essential uniqueness of an invariant integral on every compact Hausdorff group. Topics subsequently outlined include representations, the Peter-Weyl theory, positive definite functions, summability and convergence, spans of translates, closed ideals and invariant subspaces, spectral synthesis problems, the Hausdorff-Young theorem, and lacunarity.

Topological groups. --- Harmonic analysis. --- Integrals, Generalized. --- Calculus, Integral --- Analysis (Mathematics) --- Functions, Potential --- Potential functions --- Banach algebras --- Calculus --- Mathematical analysis --- Mathematics --- Bessel functions --- Fourier series --- Harmonic functions --- Time-series analysis --- Groups, Topological --- Continuous groups --- Topological Groups --- Harmonic analysis --- Integrals, Generalized

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Functional integration successfully entered physics as path integrals in the 1942 Ph.D. dissertation of Richard P. Feynman, but it made no sense at all as a mathematical definition. Cartier and DeWitt-Morette have created, in this book, a fresh approach to functional integration. The book is self-contained: mathematical ideas are introduced, developed, generalised and applied. In the authors' hands, functional integration is shown to be a robust, user-friendly and multi-purpose tool that can be applied to a great variety of situations, for example: systems of indistinguishable particles; Aharonov-Bohm systems; supersymmetry; non-gaussian integrals. Problems in quantum field theory are also considered. In the final part the authors outline topics that can be profitably pursued using material already presented.

Functional analysis --- Integration, Functional. --- Functional analysis. --- Functional calculus --- Calculus of variations --- Functional equations --- Integral equations --- Functional integration --- Integrals, Generalized

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Theory of Charges

Algebraic topology --- Mathematical physics --- Measure theory. --- Measure theory --- Lebesgue measure --- Measurable sets --- Measure of a set --- Integrals, Generalized --- Measure algebras --- Rings (Algebra) --- Topologie algébrique --- Algebraïsche topologie.

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Intégration, Chapitre 5 Les Éléments de mathématique de Nicolas BOURBAKI ont pour objet une présentation rigoureuse, systématique et sans prérequis des mathématiques depuis leurs fondements. Ce cinquième chaptire du Livre d’Intégration, sixième Livre des éléments de mathématique, traite notamment d’une generalisation du théorème des Lebesgue-Fubini et du théorème de Lebesque-Nikodym. Il contient également des notes historiques. Ce volume est une réimpression de l’édition de 1967.

Integrals. --- Calculus, Integral --- Mathematics. --- Measure and Integration. --- Math --- Science --- Measure theory. --- Lebesgue measure --- Measurable sets --- Measure of a set --- Algebraic topology --- Integrals, Generalized --- Measure algebras --- Rings (Algebra)