Real and Abstract Analysis

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], orWALTERRUDIN's Principles of Mathe­ matical Analysis [2nd Ed., McGraw-Hill Book Co., New York, 1964].

Edwin Hewitt

Edwinn Hewitt is a Professor of mathematics at the University of Washington, Seattle. He is the author of over 70 research papers and co-author, with K.A. Ross, of the book ABSTRACT HARMONIC ANALYSIS. He is a member of the National Research Council, U. S. A., has been visiting professor at Uppsala, Sweden, Yale University, and the Australian National University, Canberra. He has also lectured at many universities in the United States and Europe.

Karl Stromberg

Karl Stromberg is Professor of mathematics at Kansas State University. He has authored numerous research papers on analysis. He has been a member of the National Research Council, U.S.A. He received the Erstad Award as the outstanding teacher at the University of Oregon. He ahs spent visiting years at Yale University, the University of Chicago, Uppsala University (Sweden), and the University of York (England). He has lectured at many universities in the United States and in Europe.