Probability in Banach Spaces III Proceedings of the Third Internatio

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Probability in Banach Spaces III Proceedings of the Third International Conference on Probability in Banach Spaces Held at Tufts University, Medford, USA, August 4-16,1980

Edited by A. Beck

Springer-Verlag Berlin Heidelberg New York 1981

Editor Anatole Beck Department of Mathematics University of Wisconsin Madison, WI 53706/USA

AMS Subject Classifications (1980): 60-06, 60B99

ISBN 3-540-10822-X Springer-Verlag Berlin Heidelberg New York ISBN 0-387-10822-X Springer-Verlag New York Heidelberg Berlin This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically those of translation, reprinting, re-use of illustrations, broadcasting, reproduction by photocopying machine or similar means, and storage in data banks. Under § 54 of the German Copyright Law where copies are made for other than private use, a fee is payable to "Verwertungsgesellschaft Wort", Munich.

© by Springer-Verlag Berlin Heidelberg 1981 Printed in Germany

Printing and binding: Beltz Offsetdruck, Hemsbach/Bergstr. 214113140-543210

INTRODUCTION With each passing biennium, the subject of probability in vector spaces makes more and more impressive gains. Only twentyfive years ago, there was almost nothing in print in the subject, and what did exist was mostly an observation that the methods used in finite­dimensional spaces (which were essentially the methods for one­dimensional spaces) would extend to inf initedimensional ones with a little coaxing. But there was then no program of study, and no clear reason to investigate the subject except for the Everest Principle: it was there. Even as recently as ten years ago, the subject was considered highly esoteric. There were already strong indications of the essential bonds between measure theory and geometry, indicating the essential role of each in producing theorems, but while the structure had extent, it was without very much substance. It was a mere skeleton on which really important theorems needed to be hung to create a viable body. It was only five years ago that the accomplishments of a new and gifted generation of mathematicians had accumulated to the point that the subject was ripe for its first international conference (Oberwolfach 1975). By 1978, at the second conference, the volume of work done in the intervening three years exceeded all that had gone before, and now again, we have anew flood of results in only two years. As the 1978 conference had established that no study of Probability could any longer be considered adequate without basic grounding in infinite­dimensional theory, so we now see the infinitedimensional theory reaching past the finite into the traditional applications of probability to Physics and Statistics. I would be remiss i f I did not at this time make grateful acknowledgement of the contributions of Tufts University and especially of Prof. Marjorie Hahn. in making this conference possible, and also note the generous contribution of the National Science Foundation toward some of the expenses.