A Guide to Advanced Real Analysis

A Guide to Advanced Real Analysis is an outline of the core material in the standard graduate-level real analysis course. It is intended as a resource for students in such a course as well as others who wish to learn or review the subject. On the abstract level, it covers the theory of measure and i...

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Bibliographic Details
Main Author: Folland, Gerald B.
Format: eBook Book
Language:English
Published: Providence, Rhode Island American Mathematical Society 2009
Mathematical Association of America
Edition:1
Series:Dolciani Mathematical Expositions
Subjects:
Functions of real variables
Mathematical analysis
Mathematics
ISBN:0883853434, 9780883853436
Online Access:Get full text
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Summary:A Guide to Advanced Real Analysis is an outline of the core material in the standard graduate-level real analysis course. It is intended as a resource for students in such a course as well as others who wish to learn or review the subject. On the abstract level, it covers the theory of measure and integration and the basics of point set topology, functional analysis, and the most important types of function spaces. On the more concrete level, it also deals with the applications of these general theories to analysis on Euclidean space: the Lebesgue integral, Hausdorff measure, convolutions, Fourier series and transforms, and distributions. The relevant definitions and major theorems are stated in detail. Proofs, however, are generally presented only as sketches, in such a way that the key ideas are explained but the technical details are omitted. In this way a large amount of material is presented in a concise and readable form.
Bibliography:Includes bibliographical references and index
ISBN:0883853434
9780883853436
DOI:10.5948/UPO9780883859155