We consider a locally compact group G with jointly continuous action G× Z→ Z on a locally
compact space. The finite Radon (regular Borel) measures M (G) act naturally on various …

We show that a measured G-space (X, μ), where G is a locally compact group, is amenable
in the sense of Zimmer if and only if the following two conditions are satisfied: the associated …

0. Let G be a locally compact group with unit element e and left Haar measure. Let# be a
probability measure on G.(All measures under consideration are supposed to be Radon …

Let G be a connected amenable group (thus, an extension of a connected normal solvable
subgroup R by a connected compact group K= GR). We show how to explicitly construct …

We consider a countable discrete group $\Gamma $ acting ergodically on a standard Borel
space S with quasi-invariant measure $\mu $. Let $\pi $ be a unitary representation of …

Let G be a Hausdorff locally compact group (called a group here) and let Ix be a probability
measure in M (G), the finite regular Borel measures on G. By IltzII, we will denote the total …

We analyze the structure of a continuous (or Borel) action of a connected semi-simple Lie
group G with finite center and real rank at least 2 on a compact metric (or Borel) space X …

The theorems of M. Ratner, describing the finite ergodic invariant measures and the orbit
closures for unipotent flows on homogeneous spaces of Lie groups, are extended for actions …

Let f be a one‐cocycle for a non‐singular action of a locally compact group G on a standard
measure space (Y, μ) with values in a locally compact abelian group A. If χ ɛ Â, χ (f) is a one …

1.1. Measurable actions. Let us begin by recalling some well-known facts which are needed
in order to establish the existence of the operators which are the subject of the present …