论文标题
任意Krieger类型的非语言伯努利动作
Nonsingular Bernoulli actions of arbitrary Krieger type
论文作者
论文摘要
我们证明，每个无限的amenable组都接受任何可能的克里格类型的伯努利动作，包括$ ii_ \ infty $和类型$ iii_0 $。我们获得了该结果，这是由于对近野性和krieger类型的一般结果，非词性bernoulli Action $ g \ curvearrowrowright \ prod_ {g \ in G}（x_0，μ_g）$，带有任意基本空间$ x_0 $，均适用于$ x_0 $。较早的工作重点是两个点基础空间$ x_0 = \ {0,1 \} $，其中$ ii_ \ infty $被证明不发生。
We prove that every infinite amenable group admits Bernoulli actions of any possible Krieger type, including type $II_\infty$ and type $III_0$. We obtain this result as a consequence of general results on the ergodicity and Krieger type of nonsingular Bernoulli actions $G \curvearrowright \prod_{g \in G} (X_0,μ_g)$ with arbitrary base space $X_0$, both for amenable and for nonamenable groups. Earlier work focused on two point base spaces $X_0 = \{0,1\}$, where type $II_\infty$ was proven not to occur.
