Coboundaries of commuting Borel automorphisms | Zendy

Shrey Sanadhya | Zendy

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Coboundaries of commuting Borel automorphisms

Author(s) -

Shrey Sanadhya

Publication year - 2021

Publication title -

opuscula mathematica

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.481

H-Index - 16

eISSN - 2300-6919

pISSN - 1232-9274

DOI - 10.7494/opmath.2021.41.5.667

Subject(s) - mathematics , automorphism , borel equivalence relation , lemma (botany) , bounded function , action (physics) , borel set , space (punctuation) , pure mathematics , combinatorics , borel measure , discrete mathematics , mathematical analysis , probability measure , linguistics , ecology , philosophy , physics , poaceae , quantum mechanics , biology

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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