  Dan Rudolph showed that for an amenable group $\Gamma$, the generic
measure-preserving action of $\Gamma$ on a Lebesgue space has zero entropy.
Here this is extended to nonamenable groups. In fact, the proof shows that
every action is a factor of a zero entropy action! This uses the strange
phenomena that in the presence of nonamenability, entropy can increase under a
factor map. The proof uses Seward's recent generalization of Sinai's Factor
Theorem, the Gaboriau-Lyons result and my theorem that for every nonabelian
free group, all Bernoulli shifts factor onto each other.
