An inclusion of von Neumann factors $M \subset \Cal M$ is {\it ergodic} if it satisfies the irreducibility condition $M'\cap \Cal M=\Bbb C$. We investigate the relation between this and several stronger ergodicity properties, such as $R$-{\it ergodicity}, which requires $M$ to admit an embedding of the hyperfinite II$_1$ factor $R\hookrightarrow M$ that's ergodic in $\Cal M$. We prove that if $M$ is {\it continuous} (i.e., non type I) and contains a maximal abelian $^*$-subalgebra of $\Cal M$, then $M\subset \Cal M$ is $R$-ergodic. This shows in particular that any continuous factor contains an ergodic copy of $R$. Some related questions are discussed.

中文翻译：

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关于因子的遍历嵌入

包含冯诺依曼因子 $M \subset \Cal M$ 是 {\it ergodic} 如果它满足不可约条件 $M'\cap \Cal M=\Bbb C$。我们研究了这与几个更强的遍历性属性之间的关系，例如 $R$-{\it 遍历性}，这需要 $M$ 承认超有限 II$_1$ 因子 $R\hookrightarrow M$ 的嵌入在$\Cal M$。我们证明如果$M$是{\it连续}（即非类型I）并且包含$\Cal M$的最大阿贝尔$^*$-子代数，则$M\subset \Cal M$是$R $-遍历。这特别表明任何连续因子都包含 $R$ 的遍历副本。讨论了一些相关的问题。