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AuthorHewitt, Edwin. author
TitleReal and Abstract Analysis [electronic resource] : A modern treatment of the theory of functions of a real variable / by Edwin Hewitt, Karl Stromberg
ImprintBerlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 1965
Connect tohttp://dx.doi.org/10.1007/978-3-642-88047-6
Descript VIII, 476 p. 9 illus. online resource

SUMMARY

This book is first of all designed as a text for the course usually called "theory of functions of a real variable". This course is at present cusยญ tomarily offered as a first or second year graduate course in United States universities, although there are signs that this sort of analysis will soon penetrate upper division undergraduate curricula. We have included every topic that we think essential for the training of analysts, and we have also gone down a number of interesting bypaths. We hope too that the book will be useful as a reference for mature mathematicians and other scientific workers. Hence we have presented very general and complete versions of a number of important theorems and constructions. Since these sophisticated versions may be difficult for the beginner, we have given elementary avatars of all important theorems, with approยญ priate suggestions for skipping. We have given complete definitions, exยญ planations, and proofs throughout, so that the book should be usable for individual study as well as for a course text. Prerequisites for reading the book are the following. The reader is assumed to know elementary analysis as the subject is set forth, for example, in TOM M. ApOSTOL'S Mathematical Analysis [Addison-Wesley Publ. Co., Reading, Mass., 1957], or WALTER RUDIN'S Principles of Matheยญ nd matical Analysis [2 Ed., McGraw-Hill Book Co., New York, 1964]


CONTENT

One: Set Theory and Algebra -- Two: Topology and Continuous Functions -- Three: The Lebesgue Integral -- Four: Function Spaces and Banach Spaces -- Five: Differentiation -- Six: Integration on Product Spaces -- Index of Symbols -- Index of Authors and Terms


Mathematics Mathematical analysis Analysis (Mathematics) Harmonic analysis Functions of real variables Mathematics Analysis Abstract Harmonic Analysis Real Functions



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