Real and Abstract Analysis

1. Front Matter

   Pages I-VIII

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2. Set Theory and Algebra

   • Edwin Hewitt, Karl Stromberg

   Pages 1-52

3. Topology and Continuous Functions

   • Edwin Hewitt, Karl Stromberg

   Pages 53-103

4. The Lebesgue Integral

   • Edwin Hewitt, Karl Stromberg

   Pages 104-187

5. Function Spaces and Banach Spaces

   • Edwin Hewitt, Karl Stromberg

   Pages 188-255

6. Differentiation

   • Edwin Hewitt, Karl Stromberg

   Pages 256-376

7. Integration on Product Spaces

   • Edwin Hewitt, Karl Stromberg

   Pages 377-459

8. Back Matter

   Pages 460-476

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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].

• calculus
• function
• measure
• proof
• theorem
• variable

• The University of Washington, USA

  Edwin Hewitt

• The University of Oregon, USA

  Karl Stromberg

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