Elements of Mathematics Integration I
Intégration is the sixth and last of the Books that form the core of the Bourbaki series; it draws abundantly on the preceding five Books, especially General Topology and Topological Vector Spaces, making it a culmination of the core six. The p
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NICOLAS BOURBAKI ELEMENTS OF MATHEMATICS
Integration I Chapters 1-6 Translated by Sterling K. Berberian
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Springer
Originally published as Integration @N. Bourbaki Chapters 1 to 4, 1965 Chapter 5, 1967 Chapter 6, 1959 Translated by Sterling K. Berberian, Prof. Emeritus The University ofTexas at Austin USA
Mathematics Subject Classification (2000): 28-01, 28Bxx, 46Exx Cataloging-in-Publication Data applied for A catalog record for this book is available from the I.Jbrary of Congress. Bibliographic information published by Die Deutsche Bibliothek Die Deutsche Bibliothek lists this publication in the Deutsche Nationalbibliografie; detailed bibliographic data is available in the Internet at http://dnb.ddb.de
ISBN-13:978-3-642-63930-2 e-ISBN-13:978-3-642-59312-3 DOl: 10.1007/978-3-642-59312-3 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, broadcasting, reproduction on microfilm 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. Violations are liable for prosecution under the German Copyright Law. Springer-Verlag Berlin Heidelberg New York a member of BertelsmannSpringer Science+Business Media GmbH http://www.springer.de @ Springer-Verlag Berlin Heidelberg 2004 Softcover reprint of the hardcover 1st edition 2004 The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Typesetting: by the Translator Cover Design: Design & Production GmbH, Heidelberg Printed on acid-free paper 4113142 db 543210
To the reader
1. The Elements of Mathematics series takes up mathematics at their beginning, and gives complete proofs. In principle, it requires no particular knowledge of mathematics on the reader's part, but only a certain familiarity with mathematical reasoning and a certain capacity for abstract thought. Nevertheless, it is directed especially to those who have a good knowledge of at least the content of the first year or two of a university mathematics course. 2. The method of exposition we have chosen is axiomatic, and normally proceeds from the general to the particular. The demands of proof impose a rigorously fixed order on the subject matter. It follows that the utility of certain considerations will not be immediately apparent to the reader unless he already has a fairly extensive knowledge of mathematics. 3. The series is divided into Books, and each Book into chapters. The Books already published, either in whole or in part, in the French edition, are l
