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Lecture Notes in Mathematics A collection of informal reports and seminars Edited by A. Dold, Heidelberg and B. Eckmann, ZUrich 296 Probability and Information Theory I! Edited by M. Behara, McMaster University, Hamilton, Ontario/Canada K. Krickeberg, Universit~t Bielefeld, Bielefeld/BRD and Universit6 Ren6 Descartes, Paris/France J. Wolfowitz, University of Illinois, Urbana, IL/USA Springer-Verlag Berlin-Heidelberg- New York 1973 A M S Subject Classifications (1970): 6 0 G 3 5 , 6 0 G 9 9 , 6 2 M 1 5 , 6 2 B 10, 6 2 C 0 5 , 6 2 C 2 5 , 9 4 A I5 I S B N 3-540-06211-4 S p r i n g e r - V e r l a g B e r l i n . H e i d e l b e r g • N e w Y o r k I S B N 0-387-06211-4 S p r i n g e r - V e r l a g N e w Y o r k • H e i d e l b e r g . B e r l i n 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 the publisher, the amount of the fee to be determined by agreement with the publisher. @ by Springer Verlag Berlin - Heidelberg 1973. Library of Congress Catalog Card Number 75-406171. Printed in Germany. Offsetdruck: Julius Beltz, Hemsbach/Bergstr. PREFACE Interest in Probability and Information Theory, Proceedings of the International Symposium at McMaster University, Canada, April, (Lecture Notes in Mathematics, vol. 89 (1969) The deteriorating financial situation, ]968 ) was rather widespread. on the other hand, made it impossible for us to organize another symposium in Probability and Information Theory. In order to keep interest in the field alive and in view of the success achieved by the first volume, the second volume has been prepared. This volume contains papers based on invited lectures given by the authors at seminars sponsored jointly by McMaster University and the University of Montreal. It is a great pleasure to acknowledge the cooperation and support of Professor N.C. Girl of the University of Montreal for the organization of the seminars. Our thanks go to Professor T. Husain, Chairman of the Mathematics Department at McMaster and Professors R.G. Lintz and B.J.W. Mfilier for their overall support. We gratefully acknowledge major financial support from the National Research Council of Canada. We are greatly indebted to Professor A.N. Bourns, F.R.S.C., President of McMaster University for his keen interest in these projects. Our special thanks go to Professor M. Kac of Rockefeller University for his valuable advice on editorial matters. The Editors TABLE OF C O N T E N T S A. R~NYI: Uniform Flows in Cascade Graphs . . . . . . . . . . . . . . . W. y o n W A L D E N F E L S : A n A p p r o a c h to the T h e o r y of P r e s s u r e B r o a d e n i n g of S p e c t r a l Lines . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 K. K R I C K E B E R G : M o m e n t s of Point 7O Processes . . . . . . . . . . . . . . . . . . M. BEHARA~ P. NATH: A d d i t i v e and N o n - A d d i t i v e E n t r o p i e s of Finite M e a s u r a b l e Partitions . . . . . . . . . . . . . . . . . . . . . . . . . 102 N. GIRl: On D i s c r i m i n a n t D e c i s i o n F u n c t i o n in C o m p l e x G a u s s i a n Distributions . . . . . . . . . . . . . . . . . . . . . . . . 139 M. CSORG0: G l i v e n k 0 - C a n t e l l i Type T h e o r e m s for