Hilbert Space and Elements of Fourier Analysis
The basic tools of analysis rely on the translation invariance properties of functions and operations on Euclidean space, and, at least for applications involving integration, Fourier analysis is one of the most powerful techniques for exploiting translat
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Daniel W. Stroock
Essentials of Integration Theory for Analysis Second Edition
Graduate Texts in Mathematics
262
Graduate Texts in Mathematics Series Editors Sheldon Axler San Francisco State University, San Francisco, CA, USA Kenneth Ribet University of California, Berkeley, CA, USA Advisory Editors Alejandro Adem, University of British Columbia David Eisenbud, University of California, Berkeley & MSRI Brian C. Hall, University of Notre Dame Patricia Hersh, University of Oregon J. F. Jardine, University of Western Ontario Jeffrey C. Lagarias, University of Michigan Eugenia Malinnikova, Stanford University Ken Ono, University of Virginia Jeremy Quastel, University of Toronto Barry Simon, California Institute of Technology Ravi Vakil, Stanford University Steven H. Weintraub, Lehigh University Melanie Matchett Wood, Harvard University
Graduate Texts in Mathematics bridge the gap between passive study and creative understanding, offering graduate-level introductions to advanced topics in mathematics. The volumes are carefully written as teaching aids and highlight characteristic features of the theory. Although these books are frequently used as textbooks in graduate courses, they are also suitable for individual study.
More information about this series at http://www.springer.com/series/136
Daniel W. Stroock
Essentials of Integration Theory for Analysis Second Edition
123
Daniel W. Stroock Department of Mathematics Massachusetts Institute of Technology Cambridge, MA, USA
ISSN 0072-5285 ISSN 2197-5612 (electronic) Graduate Texts in Mathematics ISBN 978-3-030-58477-1 ISBN 978-3-030-58478-8 (eBook) https://doi.org/10.1007/978-3-030-58478-8 Mathematics Subject Classification: 28-00, 26A42 1st edition: © Springer Science+Business Media, LLC 2011 2nd edition: © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2020 This work is subject to copyright. All rights are solely and exclusively licensed 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, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral
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