Compact families and typical entropy invariants of measure-preserving actions

Ryzhikov, V.

doi:10.1090/mosc/321

Compact families and typical entropy invariants of measure-preserving actions
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by V. V. Ryzhikov
Translated by: E. I. Khukhro

Trans. Moscow Math. Soc. 2021, 117-123

DOI: https://doi.org/10.1090/mosc/321

Published electronically: March 15, 2022

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Abstract:

For a compact set of actions, an entropy of Kushnirenko type is chosen in such a way that it vanishes on this set but takes infinite values for the typical actions. As a consequence we find that typical measure-preserving transformations are not isomorphic to isometric rearrangements of a finite set of geometric figures.

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