Coboundaries of commuting Borel automorphisms

Abstract

We show that if $S,T$ are two commuting automorphisms of standard Borel space such that they generate a free Borel $\Z^2$-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 $\Z^d$-actions.