This third volume concludes our introduction to analysis, wherein we
?nish laying the groundwork needed for further study of the subject. As
with the ?rst two, this volume contains more material than can treated
in a single course. It is therefore important in preparing lectures to
choose a suitable subset of its content; the remainder can be treated in
seminars or left to independent study. For a quick overview of this
content, consult the table of contents and the chapter introductions.
Thisbookisalsosuitableasbackgroundforothercoursesorforselfstudy. We hope
that its numerous glimpses into more advanced analysis will arouse
curiosity and so invite students to further explore the beauty and scope
of this branch of mathematics. In writing this volume, we counted on the
invaluable help of friends, c- leagues, sta?, and students. Special
thanks go to Georg Prokert, Pavol Quittner, Olivier Steiger, and
Christoph Walker, who worked through the entire text cr- ically and so
helped us remove errors and make substantial improvements. Our thanks
also goes out to Carlheinz Kneisel and Bea Wollenmann, who likewise read
the majority of the manuscript and pointed out various inconsistencies.
Without the inestimable e?ortofour "typesetting perfectionist", this
volume could not have reached its present form: her tirelessness and
patience with T X E and other software brought not only the end product,
but also numerous previous versions, to a high degree of perfection. For
this contribution, she has our greatest thanks.
