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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.
21062001
Inder Jeet Taneja
Departamento de Matemática  UFSC
88.040900 Florianópolis, SC  Brazil