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## Entropy of kind t

Arimoto (1971) [3] considered generalized entropies involving a real function  with some conditions (see section 3.5.4). Being an example of these generalized entropies, Arimoto came up to a generalized entropy involving a real parameter, here we call it, entropy of kind t, given by
 (3.5)
for all . In this case also, we can easily verify that

Arimoto's main motivation in considering generalizedentropies was to prove some important results on decision theory connected with bayesian probability of error.

21-06-2001
Inder Jeet Taneja
Departamento de Matemática - UFSC
88.040-900 Florianópolis, SC - Brazil