On the entropy and generators of dynamical systems (Q678367)

The reviewed paper deals with dynamical systems and their entropy. It offers a continuation of the series of classical results on relation between the entropy of such system and the entropy of the partition of the corresponding probability space. Due to them, for a dynamic system mapping a probability space into itself its entropy is equal to the entropy of a partition of its basic set whenever the partition generates its \(\sigma\)-algebra. The main result of the paper shows that a similar result is valid even if a probability space with fuzzy \(\sigma\)-algebra is considered and the basic space is parted by a fuzzy partition generating that fuzzy \(\sigma\)-algebra.