Analytic Function Methods in Probability Theory: Colloquium - download pdf or read online

By B. Gyires

ISBN-10: 0444853332

ISBN-13: 9780444853332

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Extra info for Analytic Function Methods in Probability Theory: Colloquium Proceedings (Colloquia mathematica Societatis Janos Bolyai ; 21)

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Alexandroff, Additive set-functions in abstract spaces, a) Mat. b) Mat. Sbornik, 9(1941), 563-628, c) Mat. 13(1943), [2] H. Sbornik, 169-238. Bergstrom, Limit Theorems for Convolutions, Almqvist & Wiksell, New YorklLondon, H. Sbornik, 8(1940),307-348, Stockholm, John Wiley & Sons, 1963. Bergstrom Dept. , Chalmers Univ. of Techn. and University of Goteborg 40220 Goteborg, Sweden - 42 - COLLOQUIA HATHEMATICA SOCIETATIS JANOS BOLYAI 21. ANALYTIC FUNCTION METHODS IN PROBABILITY THEORY DEBRECEN (HUNGARY), 1977.

430-438. Csorgo and L. Stacho Bolyai Inst. of Jozsef A. Aradi vertanuk tere I, University 6722 Szeged, Hungary - 65 - , COLLOQUIA MATHEMATICA SOCIETATIS JANOS BOLYAI 21. ANALYTIC FUNCTION METHODS IN PROBABILITY THEORY DEBRECEN (HUNGARY). 1977. NONNEGATIVE INFORMATION FUNCTIONS Z. DAR6CZY - GY. HAKSA I. INTRODUCTION The notion of information functions has been introduced by Z. DAR6CZY [3J. A summary of the investigations concerning information functions can be found in the book [IJ by J. ACZ~L and Z.

DIDERRICH [5J in another direction: bounded in [0, I] If the information function then f (x) =S (x) for f is x E [ 0, I] • In this paper we prove two essential results which solve the problem of J. Aczel and Z. Daroczy. e. = inf {f (x) x E [ 0, I] where J+ denotes the class of non- negative information functions. Then we show that there exist nonnegative information functions different from the Shannon information function, that is J +"* {s} . Finally we give a negative answer to a question of P.

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Analytic Function Methods in Probability Theory: Colloquium Proceedings (Colloquia mathematica Societatis Janos Bolyai ; 21) by B. Gyires


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