Annali di Matematica Pura ed Applicata

, Volume 101, Issue 1, pp 355–373 | Cite as

Entropies with the branching property

  • B. Forte
  • C. T. Ng


It is proved that every entropy with the property of branching has the form\(\sum\limits_{i = 1}^u {f[J(A_i )] - f(0)} \), where J is a compositive information measure under a regular binary operation. In particular all the classical entropies with the branching property such as that of Shannon have the form\(\sum\limits_{i = 1}^u {f(p_i ) - F(1)} \).


Binary Operation Information Measure Compositive Information Classical Entropy 
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Si dimostra che ogni entropia che goda della proprietà di diramazione ha necessariamente la forma\(\sum\limits_{i = 1}^u {f[J(A_i )] - f(0)} \) dove J è una misura di informazione compositiva con una operazione binaria regolare. In particolare tutte le entropie classiche che godono della proprietà di diramazione quale quella di Shannon hanno la forma\(\sum\limits_{i = 1}^u {f(p_i ) - F(1)} \).


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Copyright information

© Fondazione Annali di Matematica Pura ed Applicata 1974

Authors and Affiliations

  • B. Forte
    • 1
  • C. T. Ng
    • 1
  1. 1.WaterlooCanada

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