  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
$R$.
