The Sweeping Operation
Throughout this chapter D is a Greenian subset of ℝ N , coupled with a boundary ∂D provided by a metric compactification when a boundary is relevant, and the boundary of a subset of D ∪ ∂D is that relative to the compactification. In most of the discussio
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Born in Cincinnati, Ohio on February 27, 1910, Joseph L. Doob studied for both his undergraduate and doctoral degrees at Harvard University. He was appointed to the University of Illinois in 1935 and remained there until his retirement in 1978. Doob worked first in complex variables, then moved to probability under the initial impulse of H. Hotelling, and influenced by A.N Kolmogorov's famous mono graph of 1933, as weIl as by Paul Levy's work. In his own book Stochastic Processes (1953), Doob established martingales as a particulady important type of stochastic process. Kakutani's treatment of the Dirichlet problem in 1944, combining complex variable theory and probability, sparked off Doob's interest in potential theory, which culminated in the present book. (For more details see: http://www.dartmouth.edu/ - chance/Doob/conversation.html)
Joseph l. Doob
Classical Potential Theory and Its Probabilistic Counterpart Reprint of the 1984 Edition
Springer
Joseph L. Doob University of nIinois Department of Mathematics 101 West Windsor Road 11104 Urbana, IL 61802
USA
e-mail: [email protected]
Originally published as Vol. 262 of the
Grundlehren der mathematischen Wissenschaften
Cataloging-in-Publication Deta applicd for Die DeutJche Bibliothek - CIP-EinheitaauCoahme Doob. Joseph 1..: Clauical potential theory and its probabiliatic counterpart I J. 1.. Doob. - Reprint ofthe 1984 ed. - BerIin; Heidelberg; NewYorlc; Barcelona; Hong Koog; London; Milan; Paris; SingapoR; Thkyo: Springer.2001 (Classics in mathematics) ISBN 978-3-540-41206-9 ISBN 978-3-642-56573-1 (eBook) DOI 10.1007/978-3-642-56573-1
Mathematics Subject Classification (2000): 31-xx, 6OJ45 ISSN 1431-0821 ISBN 978-3-540-41206-9 This work is 8ubject to copyright All rights are reserved, whether the whole or part of the material is concerned, speclfically the rights of translation, reprinting. reuse of illustrations. recitation, broadcasting. reproduction on miaofilm or in any other war. Ind storage in deta blnb. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9.1965. in its rumnt venion, and permission for use must alwayI be obtaincd from Springer-Verlag. Violations Ire liable for prosec:ution under the German Copyright Law.
CI Springer-Verlag Berlin Heidelberg 2001 Originally published by Springer-Verlag Berlin Heidelberg NewYork in
2001
The use of general descriptive names, registered names, trademarks etc. in this publication does not imply. even in the absence of a speclfic statement, tbat such names are uempt from the relevant protective laws and regulations Ind therefore free for general use. Printed on acid-free paper
SPIN 10786705
4113142ck-543210
J. L. Doob
Classical Potential Theory and Its Probabilistic Counterpart
Springer Science+ Business Media, LLC
J. L. Doob
Department of Mathematics University of Illinois Urbana, IL 61801 U.S.A.
AMS Subject Classificaticns: 31-XX, 6OJ45 Library of Congress Cataloging in Publication Data Doob, Joseph L. Class
