Geodesic
Estimating the asymptotic behavior of the entropy of an invariant sequence of partitions of the infinite-dimensional cube
Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial and algoritmic methods. Part XXX, Tome 481 (2019), pp. 5-11 
G. A. Veprev. Estimating the asymptotic behavior of the entropy of an invariant sequence of partitions of the infinite-dimensional cube. Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial and algoritmic methods. Part XXX, Tome 481 (2019), pp. 5-11. http://geodesic.mathdoc.fr/item/ZNSL_2019_481_a0/
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     author = {G. A. Veprev},
     title = {Estimating the asymptotic behavior of the entropy of an invariant sequence of partitions of the infinite-dimensional cube},
     journal = {Zapiski Nauchnykh Seminarov POMI},
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     year = {2019},
     volume = {481},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2019_481_a0/}
}
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

In this paper, we solve the question, posed by A. M. Vershik, about the asymptotic behavior of the entropies of a given sequence of partitions of the infinite-dimensional cube satisfying the invariance and exhaustibility properties. On the one hand, it is proved that the entropy sequence increases faster than a linear function. On the other hand, we construct a series of examples that show that the estimate is sharp: for any given sequence increasing faster than a linear function, the entropy of a sequence of partitions can increase slower than the given sequence.

[1] A. M. Vershik, “Asimptotika razbieniya kuba na simpleksy Veilya i kodirovanie skhemy Bernulli”, Funkts. anal. i pril., 53:2 (2019), 11–31 | DOI | MR | Zbl

[2] V. A. Rokhlin, “Lektsii po entropiinoi teorii preobrazovanii s invariantnoi meroi”, Uspekhi mat. nauk, 22:5(137) (1967), 3–56 | MR | Zbl