The Rohlin tower theorem and hyper-finiteness for actions of continuous groups

We prove the Rohlin tower theorem for free measure preserving actions of locally compact second countable solvable groups and almost connected amenable groups. This theorem was known for l.c.s.c. abelian groups and was recently extended by Ornstein and Weiss to discrete solvable groups. We extend their methods to the continuous case, using the structure theory of the class of groups under consideration. As a corollary we obtain that free actions of such groups generate hyperfinite equivalence relations. Work supported in part by NSF grant MCS 74-19876. A02.