Continuity of measurable cocycles

Abstract

Suppose $G\curvearrowright X$ is a Polish group action, $H$ is a Polish group and $G\times X\stackrel{\ddot{I}}{ˆ}⟶H$ is a cocycle that is continuous in the second variable. If $\ddot{I}ˆ$ is either Baire measurable or is $\hat{I}»\times \hat{I}¼$-measurable with respect to a Haar measure $\hat{I}»$ on $G$ and a fully supported $\ddot{I}ƒ$-finite Borel measure $\hat{I}¼$ on $X$, then $\ddot{I}ˆ$ is jointly continuous.

This version differs from the previous one entitled "Almost homomorphisms and measurable cocycles" in several regards. First of all, the part on almost homomorphisms has been eliminated due to an overlap with the literature. Secondly, the results on measurable cocycles have been strengthened