Zeitschrift für Analysis und ihre Anwendungen
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Published online: 1982-08-31
On a Class of Generalized $K$-Entropies and Bernoulli ShiftsThomas de Paly
The paper presents the construction of an example important for the discussion of some generalizations of the $K$-entropy. These generalizations have been introduced in a previous paper. A formula for the generalized entropies of a process is calculated for the case where the process is given by a Bernoulli shift and a partition consisting only of cylinder sets. Furthermore, a special optimization problem on the set of all probability vectors of a given entropy is solved using a new method. The results of these computations are combined to the cited example.
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de Paly Thomas: On a Class of Generalized $K$-Entropies and Bernoulli Shifts. Z. Anal. Anwend. 1 (1982), 87-96. doi: 10.4171/ZAA/31