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Author : Inder K. Rana
Release : 2005
Genre : Lebesgue integral
Kind : eBook
Book Rating : 914/5 ( reviews)
Book Synopsis An Introduction to Measure and Integration by : Inder K. Rana
Download or read book An Introduction to Measure and Integration written by Inder K. Rana. This book was released on 2005. Available in PDF, EPUB and Kindle. Book excerpt:
Author : S. J. Taylor
Release : 1973-12-27
Genre : Mathematics
Kind : eBook
Book Rating : 045/5 ( reviews)
Book Synopsis Introduction to Measure and Integration by : S. J. Taylor
Download or read book Introduction to Measure and Integration written by S. J. Taylor. This book was released on 1973-12-27. Available in PDF, EPUB and Kindle. Book excerpt: This paperback, gives a self-contained treatment of the theory of finite measures in general spaces at the undergraduate level.
Author : Terence Tao
Release : 2021-09-03
Genre : Education
Kind : eBook
Book Rating : 406/5 ( reviews)
Book Synopsis An Introduction to Measure Theory by : Terence Tao
Download or read book An Introduction to Measure Theory written by Terence Tao. This book was released on 2021-09-03. Available in PDF, EPUB and Kindle. Book excerpt: This is a graduate text introducing the fundamentals of measure theory and integration theory, which is the foundation of modern real analysis. The text focuses first on the concrete setting of Lebesgue measure and the Lebesgue integral (which in turn is motivated by the more classical concepts of Jordan measure and the Riemann integral), before moving on to abstract measure and integration theory, including the standard convergence theorems, Fubini's theorem, and the Carathéodory extension theorem. Classical differentiation theorems, such as the Lebesgue and Rademacher differentiation theorems, are also covered, as are connections with probability theory. The material is intended to cover a quarter or semester's worth of material for a first graduate course in real analysis. There is an emphasis in the text on tying together the abstract and the concrete sides of the subject, using the latter to illustrate and motivate the former. The central role of key principles (such as Littlewood's three principles) as providing guiding intuition to the subject is also emphasized. There are a large number of exercises throughout that develop key aspects of the theory, and are thus an integral component of the text. As a supplementary section, a discussion of general problem-solving strategies in analysis is also given. The last three sections discuss optional topics related to the main matter of the book.
Author : Luigi Ambrosio
Release : 2012-02-21
Genre : Mathematics
Kind : eBook
Book Rating : 869/5 ( reviews)
Book Synopsis Introduction to Measure Theory and Integration by : Luigi Ambrosio
Download or read book Introduction to Measure Theory and Integration written by Luigi Ambrosio. This book was released on 2012-02-21. Available in PDF, EPUB and Kindle. Book excerpt: This textbook collects the notes for an introductory course in measure theory and integration. The course was taught by the authors to undergraduate students of the Scuola Normale Superiore, in the years 2000-2011. The goal of the course was to present, in a quick but rigorous way, the modern point of view on measure theory and integration, putting Lebesgue's Euclidean space theory into a more general context and presenting the basic applications to Fourier series, calculus and real analysis. The text can also pave the way to more advanced courses in probability, stochastic processes or geometric measure theory. Prerequisites for the book are a basic knowledge of calculus in one and several variables, metric spaces and linear algebra. All results presented here, as well as their proofs, are classical. The authors claim some originality only in the presentation and in the choice of the exercises. Detailed solutions to the exercises are provided in the final part of the book.
Author : Frank Burk
Release : 2011-10-14
Genre : Mathematics
Kind : eBook
Book Rating : 982/5 ( reviews)
Book Synopsis Lebesgue Measure and Integration by : Frank Burk
Download or read book Lebesgue Measure and Integration written by Frank Burk. This book was released on 2011-10-14. Available in PDF, EPUB and Kindle. Book excerpt: A superb text on the fundamentals of Lebesgue measure and integration. This book is designed to give the reader a solid understanding of Lebesgue measure and integration. It focuses on only the most fundamental concepts, namely Lebesgue measure for R and Lebesgue integration for extended real-valued functions on R. Starting with a thorough presentation of the preliminary concepts of undergraduate analysis, this book covers all the important topics, including measure theory, measurable functions, and integration. It offers an abundance of support materials, including helpful illustrations, examples, and problems. To further enhance the learning experience, the author provides a historical context that traces the struggle to define "area" and "area under a curve" that led eventually to Lebesgue measure and integration. Lebesgue Measure and Integration is the ideal text for an advanced undergraduate analysis course or for a first-year graduate course in mathematics, statistics, probability, and other applied areas. It will also serve well as a supplement to courses in advanced measure theory and integration and as an invaluable reference long after course work has been completed.
