The equivalence between different characterizations of amenable actions of a locally compact group is proved. In particular, this answers a question raised by R. J. Zimmer in 1977. 0. Introductionâ€¦ (More)

Let a connected real Lie group G act on a C 8 real manifold M , and assume that the action is both C 8 and effective on every nonempty G-invariant open set. We show that there is a nonemptyâ€¦ (More)

The main theorems below are Theorem 9 and Theorem 11. As far as I know, Theorem 9 represents a slight improvement over what currently appears in the literature, and gives a fairly easy proof ofâ€¦ (More)

We prove that an effective, analytic action of a connected Lie group G on a manifold M becomes free on a comeager subset of an open subset when prolonged to both frame bundles and jet bundles over Mâ€¦ (More)

ACKNOWLEDGEMENTS As is appropriate, the major influence on my mathematical development in the past few years has been that exerted by Robert J. Zimmer. Enthusiastically, I thank him for providingâ€¦ (More)