Postmodern Analysis
What is the title of this book intended to signify, what connotations is the adjective "Postmodern" meant to carry? A potential reader will surely pose this question. To answer it, I should describe what distinguishes the approach to analysis presented he
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Springer-Verlag Berlin Heidelberg GmbH
Jürgen Jost
Postmodern
Analysis
Translated by Hassan Azad With 13 Figures and Numerous Exercises
Springer
Jürgen Jost Max Planck Institute for Mathematics in the Sciences Inselstr. 22-26 D-04103 Leipzig Germany HassanAzad Department of Mathematical Sciences King Fahd University 31261 Dhahran Saudi Arabia
Title of the German manuscript: Postmoderne Analysis The cover picture shows example 2 on page 112.
Mathematics Subject Classification (1991): 26-01, 46-01, 49-01
Library of Congress Cataloging-in Publication Oata
Jost. JÜrgen. 1956Postlodern analysis I Jürgen Jost. p. cm. -- (Universitext) ISBN 978-3-540-63485-0 ISBN 978-3-662-03635-8 (eBook) DOI 10.1007/978-3-662-03635-8 1. Mathematical analysis. I. Title.
CA300.J83 515--dc21
1998
97-37167 CIP
This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation. broad-casting, reproduction on microfilms or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965. in its current version, and permission for use must always be obtained from Springer-Verlag Berlin Heidelberg GmbH. Violations are liable for prosecution under the German Copyright Law. © Springer-Verlag Berlin Heidelberg 1998
Originally published by Springer-Verlag Berlin Heidelberg New York in 1998 Electronic editing and formatting of the author's TEX fIles by Springer-Verlag. Cover design: design 6- production GmbH. Heidelberg
SPIN: 10121379
41/3143 - 5 4 3 21 0 - Printed on acid-free paper
To Eberhard Zeidler,
for building up our Institute with so much enthusiasm and human skill
Preface
What is the title of this book intended to signify, what connotations is the adjective "Postmodern" meant to carry? A potential reader will surely pose this question. To answer it, I should describe what distinguishes the approach to analysis presented here from what has been called "Modern Analysis" by its protagonists. "Modern Analysis" as represented in the works of the Bourbaki group or in the textbooks by Jean Dieudonne is characterized by its systematic and axiomatic treatment and by its drive towards a high level of abstraction. Given the tendency of many prior treatises on analysis to degenerate into a collection of rather unconnected tricks to solve special problems, this definitively represented a healthy achievement. In any case, for the development of a consistent and powerful mathematical theory, it seems to be necessary to concentrate solelyon the internal problems and structures and to neglect the relations to other fields of scientific, even of mathematical study for a certain while. Almost complete isolation may be required to reach the level of intellectual elegance and perfection that only a good mathematical theory can acquire. However, once this level has been reached, it might b
