Coboundaries of commuting Borel automorphisms
We show that if \(S\), \(T\) are two commuting automorphisms of a standard Borel space such that they generate a free Borel \(\mathbb{Z}^2\)-action then \(S\) and \(T\) do not have same sets of real valued bounded coboundaries. We also prove a weaker form of Rokhlin Lemma for Borel \(\mathbb{Z}^d\)-...
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| Format: | Article |
| Language: | English |
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AGH Univeristy of Science and Technology Press
2021-09-01
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| Series: | Opuscula Mathematica |
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| Online Access: | https://www.opuscula.agh.edu.pl/vol41/5/art/opuscula_math_4132.pdf |
| Summary: | We show that if \(S\), \(T\) are two commuting automorphisms of a standard Borel space such that they generate a free Borel \(\mathbb{Z}^2\)-action then \(S\) and \(T\) do not have same sets of real valued bounded coboundaries. We also prove a weaker form of Rokhlin Lemma for Borel \(\mathbb{Z}^d\)-actions. |
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| ISSN: | 1232-9274 |