Remarks on the tightness of cocycles
Volume 84 / 2000
Colloquium Mathematicum 84 (2000), 363-376
DOI: 10.4064/cm-84/85-2-363-376
Abstract
We prove a generalised tightness theorem for cocycles over an ergodic probability preserving transformation with values in Polish topological groups. We also show that subsequence tightness of cocycles over a mixing probability preserving transformation implies tightness. An example shows that this latter result may fail for cocycles over a mildly mixing probability preserving transformation.