Ebook: Real and Abstract Analysis: A modern treatment of the theory of functions of a real variable
- Tags: Mathematics general
- Year: 1965
- Publisher: Springer-Verlag Berlin Heidelberg
- Edition: 1
- Language: English
- pdf
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 M athe nd matical Analysis [2 Ed., McGraw-Hill Book Co., New York, 1964].
Content:
Front Matter....Pages I-VIII
Set Theory and Algebra....Pages 1-52
Topology and Continuous Functions....Pages 53-103
The Lebesgue Integral....Pages 104-187
Function Spaces and Banach Spaces....Pages 188-255
Differentiation....Pages 256-376
Integration on Product Spaces....Pages 377-459
Back Matter....Pages 460-476
Content:
Front Matter....Pages I-VIII
Set Theory and Algebra....Pages 1-52
Topology and Continuous Functions....Pages 53-103
The Lebesgue Integral....Pages 104-187
Function Spaces and Banach Spaces....Pages 188-255
Differentiation....Pages 256-376
Integration on Product Spaces....Pages 377-459
Back Matter....Pages 460-476
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