الصفحة 1
الصفحة 1
Measure, Integration & Real Analysis
This book welcomes students into the fundamental theory of measure, integration, and real analysis. Focusing on an accessible approach, Axler lays the foundations for further study by promoting a deep understanding of key results.
Measure Theory and Probability Theory
The book can be used as a text for a two semester sequence of courses in measure theory and probability theory, with an option to include supplemental material on stochastic processes and special topics.Prerequisites are kept to the minimal level of an understanding of basic real analysis concepts such as limits, continuity, differentiability, Riemann integration, and convergence of sequences and series. A review of this material is included in the appendix. The book starts with an informal introduction that provides some heuristics into the abstract concepts of measure and integration theory, which are then rigorously developed. The first part of the book can be used for a standard real analysis course for both mathematics and statistics Ph.D. students as it provides full coverage of topics such as the construction of Lebesgue-Stieltjes measures on real line and Euclidean spaces, the basic convergence theorems, L^p spaces, signed measures, Radon-Nikodym theorem, Lebesgue's decomposition theorem and the fundamental theorem of Lebesgue integration on R, product spaces and product measures, and Fubini-Tonelli theorems. It also provides an elementary introduction to Banach and Hilbert spaces, convolutions, Fourier series and Fourier and Plancherel transforms.
Introduzione alla teoria della misura e all’analisi funzionale = Introduction to measurement theory and functional analysis
Presents a treatment of the theory of measure from an abstract point of view, with particular emphasis on some aspects of interest in probability. The typical arguments of the theory of integration are developed in a rather in-depth way, trying where possible to deduce classical results from the modern setting of the theory as well. The text has a modular structure, with interconnections between the parts: some chapters deal with theoretical aspects, others are dedicated to more applied topics. Alongside the numerous examples, a wide range of exercises is proposed.
Intégration : Chapitres 7 et 8 = Integration : Chapters 7 and 8
Nicolas BOURBAKI's Elements of Mathematics aim to provide a rigorous, systematic presentation without prerequisites of mathematics from their foundations. applications. The concepts introduced, such as Haar measures and the convolution product, are the basis of harmonic analysis. It includes the chapters: Haar measure; Convolution and representations.
Intégration : Chapitres 1 à 4 = Integration : Chapters 1 to 4
Nicolas BOURBAKI's Elements of Mathematics aim to provide a rigorous, systematic presentation without prerequisites of mathematics from their foundations. it includes the chapters: Inequalities of convexity, Riesz spaces, Measures on locally compact spaces.
Intégration : Chapitre 6 = Integration : Chapters 6
Nicolas BOURBAKI's Elements of Mathematics aim to provide a rigorous, systematic presentation without prerequisites of mathematics from their foundations.This sixth chapter of the Book of Integration, the sixth Book of the elements of mathematics, extends the notion of integration to values in locally convex Hausdorff vector spaces.
Intégration : Chapitre 5 = Integration : Chapters 5
Nicolas BOURBAKI's Elements of Mathematics aim to provide a rigorous, systematic presentation without prerequisites of mathematics from their foundations. This fifth chapter of the Book of Integration, the sixth Book of the elements of mathematics, deals in particular with a generalization of the Lebesgue theorem -Fubini and Lebesque-Nikodym's theorem. It also contains historical notes.
Eléments de Mathématique. Intégration : Chapitre 9 Intégration sur les espaces topologiques séparés
The Mathematics Elements of Nicolas BOURBAKI aim to provide a rigorous, systematic presentation without prerequisites of mathematics from their foundations. This ninth chapter of the Book of Integration, sixth Book of the elements of mathematics, is devoted to the integration in separate topological spaces not necessarily locally compact, which allows to extend the theory of the Fourier transformation to locally convex vector spaces .
