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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
Article

Summary

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\(\sum\limits_{i = 1}^u {f(p_i ) - F(1)} \).

Keywords

Binary Operation Information Measure Compositive Information Classical Entropy 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Sunto

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\(\sum\limits_{i = 1}^u {f(p_i ) - F(1)} \).

References

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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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