Geodesic
About one property of entropy of decreasing sequence of measureble partitions
Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial and algoritmic methods. Part III, Tome 256 (1999), pp. 19-24

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This work is devoted to improving of the assimptotic that appeares in the difinition of the entropy invariant of decreasing sequences of measurable partitions, introduced by A. Vershik. An example of sets that have no good approcsimation by cillinders is represented: $$ \forall\alpha_n\rightarrow 0\,\exists\gamma_0=\{A,cA\}\;\text{and}\;n_k\rightarrow\infty:H(\gamma^{n_k})>\alpha_{n_k}2^{n_k}. $$ 
@article{ZNSL_1999_256_a1,
     author = {A. Gorbulsky},
     title = {About one property of entropy of decreasing sequence of measureble partitions},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {19--24},
     publisher = {mathdoc},
     volume = {256},
     year = {1999},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1999_256_a1/}
}
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A. Gorbulsky. About one property of entropy of decreasing sequence of measureble partitions. Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial and algoritmic methods. Part III, Tome 256 (1999), pp. 19-24. http://geodesic.mathdoc.fr/item/ZNSL_1999_256_a1/