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The Branching Property in Generalized Information Theory

Bruce Ebanks
Advances in Applied Probability
Vol. 10, No. 4 (Dec., 1978), pp. 788-802
DOI: 10.2307/1426659
Stable URL: http://www.jstor.org/stable/1426659
Page Count: 15
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The Branching Property in Generalized Information Theory
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Abstract

It is shown that every measure of expected information which has the branching property is of the form Cn+∑i=1 nfn,i(J(Ai))+∑i=1 n-1(J(Ai))+∑i=1 n-1Ψ n(J(Ai),J(Ai+1)⚬ J(Ai+2)⚬ ⋯ ⚬ J(An)), where J is a given information measure which is compositive under a regular binary operation ⚬ , and the Ψ n are antisymmetric, bi-additive functions. In a probability space, such measures (entropies) take the form Cn+∑i=1 nfn,i(Pi)+∑i=1 n-1Ψ n(Pi,Pi+1+Pi+2+⋯ +Pn).

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