Analysis From Concepts to Applications
This textbook covers the main results and methods of real analysis in a single volume. Taking a progressive approach to equations and transformations, this book starts with the very foundations of real analysis (set theory, order, convergence, and measure
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Jean-Paul Penot
Analysis
From Concepts to Applications
Universitext
Universitext Series Editors Sheldon Axler San Francisco State University Vincenzo Capasso Università degli Studi di Milano Carles Casacuberta Universitat de Barcelona Angus MacIntyre Queen Mary, University of London Kenneth Ribet University of California, Berkeley Claude Sabbah CNRS, École Polytechnique, Palaiseau, France Endre Süli University of Oxford Wojbor A. Woyczy´nski Case Western Reserve University Cleveland, OH
Universitext is a series of textbooks that presents material from a wide variety of mathematical disciplines at master’s level and beyond. The books, often well classtested by their author, may have an informal, personal even experimental approach to their subject matter. Some of the most successful and established books in the series have evolved through several editions, always following the evolution of teaching curricula, to very polished texts. Thus as research topics trickle down into graduate-level teaching, first textbooks written for new, cutting-edge courses may make their way into Universitext.
More information about this series at http://www.springer.com/series/223
Jean-Paul Penot
Analysis From Concepts to Applications
123
Jean-Paul Penot Université Pierre et Marie Curie Paris, France
ISSN 0172-5939 Universitext ISBN 978-3-319-32409-8 DOI 10.1007/978-3-319-32411-1
ISSN 2191-6675 (electronic) ISBN 978-3-319-32411-1 (eBook)
Library of Congress Control Number: 2016960582 Mathematics Subject Classification (2010): 03-01, 06-AXX, 26XX, 28AXX, 34XX, 35AXX, 40-00, 46-01, 47-01, 49-00, 49-01, 54-00, 54-01, 90-01 © Springer International Publishing Switzerland 2016 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, 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. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. Printed on acid-free paper This Springer imprint is published by Springer Nature The registered company is Springer International Publishing AG Switzerland
To the memory of Hélène
Preface
Nothing is lost, nothing is created out of nothing, everything is transf
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