The Bartle-Dunford-Schwartz Integral Integration with Respect to a S
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Vol. 69 New Series
T.V. Panchapagesan
The Bartle-Dunford-Schwartz Integral Integration with Respect to a Sigma-Additive Vector Measure
Monografi e
M at em at yc z n e
Instytut Matematyczny Polskiej Akademii Nauk (IMPAN)
Volume 69 (New Series) Founded in 1932 by S. Banach, B. Knaster, K. Kuratowski, S. Mazurkiewicz, W. Sierpinski, H. Steinhaus
Managing Editor: Przemysław Wojtaszczyk, IMPAN and Warsaw University Editorial Board: Jean Bourgain (IAS, Princeton, USA) Tadeusz Iwaniec (Syracuse University, USA) Tom Körner (Cambridge, UK) Krystyna Kuperberg (Auburn University, USA) Tomasz Łuczak (Poznán University, Poland) Ludomir Newelski (Wrocław University, Poland) Gilles Pisier (Université Paris 6, France) Piotr Pragacz (Institute of Mathematics, Polish Academy of Sciences) ˛ Grzegorz ´ Swiatek (Pennsylvania State University, USA) Jerzy Zabczyk (Institute of Mathematics, Polish Academy of Sciences)
Volumes 31–62 of the series Monografie Matematyczne were published by PWN – Polish Scientific Publishers, Warsaw
T.V. Panchapagesan
The Bartle-Dunford-Schwartz Integral Integration with Respect to a Sigma-Additive Vector Measure
Birkhäuser Basel · Boston · Berlin
Author: T.V. Panchapagesan 301, Shravanthi Palace 3rd Cross, C.R.Layout J.P. Nagar, 1st Phase Bangalore 560 078 India e-mail: [email protected]
Formerly: Departamento de Matemáticas Facultad de Ciencias Universidad de los Andes Mérida 5101 Venezuela e-mail: [email protected]
2000 Mathematical Subject Classification: primary 28B05; secondary 46E40, 46G10 Library of Congress Control Number: 2007942613 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 978-3-7643-8601-6 Birkhäuser Verlag AG, Basel - Boston - Berlin 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, re-use of illustrations, recitation, broadcasting, reproduction on microfilms or in other ways, and storage in data banks. For any kind of use permission of the copyright owner must be obtained.
© 2008 Birkhäuser Verlag AG Basel · Boston · Berlin P.O. Box 133, CH-4010 Basel, Switzerland Part of Springer Science+Business Media Printed on acid-free paper produced from chlorine-free pulp. TCF ∞ Printed in Germany ISBN 978-3-7643-8601-6
e-ISBN 978-3-7643-8602-3
987654321
www.birkhauser.ch
The monograph is dedicated to the memory of the author’s spiritual guru Singaracharya Swamigal of Kondapalayam, Scholingur, and to the memory of his eldest brother T.V. Gopalaiyer, a great Tamil scholar, of Ecole Fran¸caise D’extrˆeme-Orient, Centre de Pondicherry.
Contents Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
ix
1 Preliminaries 1.1 Banach space-valued measures . . . . . . . . . . . . . . . . . . . . 1.2 lcHs-valued measures . . . . . . . . . . . . . . . . . . . .
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