Real and Abstract Analysis

K. Stromberg

ISBN 10: 3540780181 / ISBN 13: 9783540780182

Editore: Springer Berlin Heidelberg, Springer Berlin Heidelberg Jan 1980, 1980

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Neuware -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 cus 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 appro priate suggestions for skipping. We have given complete definitions, ex planations, and proofs throughout, so that the book should be usablefor 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 Mathe nd matical Analysis [2 Ed., McGraw-Hill Book Co., New York, 1964].Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 488 pp. Englisch.

Codice articolo 9783540780182

Dati bibliografici

• Titolo: Real and Abstract Analysis
• Editore: Springer Berlin Heidelberg, Springer Berlin Heidelberg Jan 1980
• Data di pubblicazione: 1980
• Lingua: Inglese
• ISBN 10: 3540780181
• ISBN 13: 9783540780182
• Rilegatura: Taschenbuch
• Condizione: Neu

Descrizione articolo

Riassunto

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 cus­ 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 appro­ priate suggestions for skipping. We have given complete definitions, ex­ 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 Mathe­ nd matical Analysis [2 Ed., McGraw-Hill Book Co., New York, 1964].

Contenuti

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.