Bernoulli convolutions and an intermediate value theorem for entropies of \(k\)-partitions (Q1809918)

The authors deal with the following question suggested by Ya. G. Sinai, that is: given a probability measure preserving system \(\widetilde X= (X,{\mathcal A},\mu, T)\), what are the possible values of the conditional entropy for \(K\)-partitions in \(X\)? Here the authors give a complete answer to Sinai's question for the case where \(X\) is a Bernoulli system, using certain concrete linear filters.