AI 中文总结
本文针对文献[ACTT23]提出的问题，证明混合无单位群的忠实广义伯努利作用及紧阿贝尔群上的仿射作用均为本质自由，拓展了具有该性质的离散遍历作用类。
AI 中文摘要
文献[ACTT23]提出：混合无单位（MIF）群的每个忠实、离散、保测度（pmp）遍历作用是否本质自由。本文给出肯定证据，证明对MIF群，任意忠实广义伯努利作用及任意紧阿贝尔群上的仿射作用均为本质自由，这提供了完全遍历或紧情况之外具有该性质的离散遍历作用类。
英文摘要
It was asked in [ACTT23] if every faithful, discrete, ergodic pmp action of a mixed identity-free (MIF) group is essentially free. In this short note we give some positive evidence by showing that for a MIF group, any faithful generalized Bernoulli action and any affine action on a compact abelian group is essentially free. This gives some classes of discrete ergodic actions with this property beyond the totally ergodic or compact case.
Comments12 pages; comments welcome
