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1391 S. Cambanis A. Weron

(Eds.)

Probability Theory on Vector Spaces IV Proceedings of a Conference, held inLaricut, Poland, June 10-17,1987

Springer-Verlag Berlin Heidelberg NewYork London ParisTokyo Hong Kong

Editors Stamatis Cambanis Department of Statistics, University of North Carolina Chapel Hill, NC 27599, USA Aleksander Weron Institute of Mathematics, Technical University of Wroclaw 50-370 Wroclaw, Poland

Mathematics Subject Classification: Primary 60 Bxx, 28Cxx Secondary46L 10, 60E07, 60G 10,60G 15, 60G25, 60G46,60H05, 81C20, 82A31 ISBN 3-540-51548-8 Springer-Verlag Berlin Heidelberg New York ISBN 0-387-51548-8 Springer-Verlag New York Berlin Heidelberg

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. Duplication of this publication or parts thereof is only permitted under the provisions of the German Copyright Law of September 9, 1965, in its version of June 24, 1985, and a copyright fee must always be paid. Violations fall under the prosecu1ion act of the German Copyright Law.

© Springer-Verlag Berlin Heidelberg 1989 Printed in Germany Printing and binding: Druckhaus Beltz, Hemsbach/Bergstr. 2146/3140-543210 - Printed on acid-free paper

Dedicated to the IIBIDry of

HUGO STEINHAUS (1887-1972) on the occasion of his 1CD-th birthday

PREFACE

This volume consists of a selection of 34 contributions presented during the international conference PROBABILITY THEORY ON VECTOR SPACES IV held in Lancut (south-eastern Poland), June 10-17, 1987. The conference, the fourth of such meetings organized in Poland during the last decade, was aimed at bringing together a group of researchers to discuss their current work on functional analysis aspects of probability theory, to provide encouragement for further research through the lectures of invited scholars, and to introduce to younger colleagues the latest research techniques in infinite dimensional probability theory. During the meeting the participants celebrated HUGO STEINHAUS's 100th birthday. The invited speakers on the special session were Z.Ciesielski and K. Urbanik. Professor Steinhaus had a world wide reputation. He was one of the founders of the internationally acknowledged "Lwow school" of functional analysis, and "Wroclaw school" of probability. It has been the aim of the editors of these Proceedings to include new and significant results. We wish to express our deep gratitude to all the referees for their indispensable help. The selected papers tie together known results of the previous proceedings volumes: Springer-Verlag's Lecture Notes in Math. vol. 656 (1978), vol. 828 (1980), and vol. 1080 (1984), describe the underlying ideas, summarize the state-of-the-art, and state some open problems. Topics covered in this volume include: PROBABILITY MEASURES ON ALGEBRAIC AND TOPOLOGICAL STRUCTURES (A. Bartoszewicz,