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 otIered 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 inc1uded 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. Rence 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 weil as for a course text.
Prerequisites for reading the book are the foilowing. 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 P1'inciplesol Mathe-
4 matical Analysis [2" Ed., McGraw-Rill Book Co., New York, 1964].
