Open AccessCoboundaries of commuting Borel automorphisms
Author(s) -
Shrey Sanadhya
Publication year - 2021
Publication title -
rocznik akademii górniczo-hutniczej im. stanisława staszica. opuscula mathematica/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 , lemma (botany) , bounded function , borel equivalence relation , action (physics) , space (punctuation) , combinatorics , borel set , pure mathematics , discrete mathematics , borel measure , mathematical analysis , probability measure , linguistics , physics , ecology , philosophy , 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.