#### 176 Citations

An uncountable Mackey-Zimmer theorem

- Mathematics
- 2020

The Mackey-Zimmer theorem classifies ergodic group extensions $X$ of a measure-preserving system $Y$ by a compact group $K$, by showing that such extensions are isomorphic to a group skew-product $X… Expand

Cocycles and continuity

- Mathematics
- 2012

The topic of this paper is the Mackey Cocycle Theorem: every Borel almost cocycle is equivalent to a Borel strict cocycle. This is a theorem about locally compact groups which is not true for… Expand

ON A STRENGTHENING OF THE HERWIG – LASCAR EXTENSION THEOREM

- 2009

The purpose of this note is to review and reorganize the proof of the Herwig–Lascar extension theorem, [2, Theorem 3.2], and to indicate how small additions to this proof can be used to obtain a… Expand

An amenable equivalence relation is generated by a single transformation

- Mathematics
- 1981

We prove that for any amenable non-singular countable equivalence relation R ⊂ X × X , there exists a non-singular transformation T of X such that, up to a null set: It follows that any two Cartan… Expand

COHERENT EXTENSION OF PARTIAL AUTOMORPHISMS, FREE AMALGAMATION AND AUTOMORPHISM GROUPS

- Mathematics, Computer Science
- The Journal of Symbolic Logic
- 2020

Abstract We give strengthened versions of the Herwig–Lascar and Hodkinson–Otto extension theorems for partial automorphisms of finite structures. Such strengthenings yield several combinatorial and… Expand

Orbit equivalence for Cantor minimal $\mathbb{Z}^{2}$-systems

- Mathematics
- 2008

We show that every minimal action of any finitely generated abelian group on the Cantor set is (topologically) orbit equivalent to an AF relation. As a consequence, this extends the classification up… Expand

Espaces mesurés singuliers fortement ergodiques (Étude métrique–mesurée)

- Mathematics
- 2007

D'apres le theoreme de Jones-Schmidt, une relation d'equivalence ergodique est fortement ergodique si et seulement si elle ne possede pas de quotient moyennable non trivial. Nous donnons dans cet… Expand

Quantized reduction as a tensor product

- Mathematics, Physics
- 2001

Symplectic reduction is reinterpreted as the composition of arrows in the category of integrable Poisson manifolds, whose arrows are isomorphism classes of dual pairs, with symplectic groupoids as… Expand

Cocycles and the structure of ergodic group actions

- Mathematics
- 1977

We show, for a large class of groups, the existence of cocycles taking values in these groups and which define ergodic skew products. We apply this to prove a generalization of Ambrose’s… Expand

#### References

SHOWING 1-10 OF 12 REFERENCES

ERGODIC THEORY, GROUP THEORY AND DIFFERENTIAL GEOMETRY.

- Mathematics, Medicine
- Proceedings of the National Academy of Sciences of the United States of America
- 1963

6Hall, B. D., and S. Spiegelman, these PROCEEDINGS, 47,137(1961). 7Nygaard, A. P., and B. D. Hall, Biochem. Biophys. Res. Comm., 12, 98 (1963). 8 Adams, M. H., Bacteriophages (New York: Interscience… Expand

On invariant measures

- Mathematics
- 1960

Given a measurable transformation on a measure space one can ask whether or not there is an equivalent measure that is invariant under the transformation. This problem is discussed very thoroughly in… Expand

Unitary representations of group extensions. I

- Mathematics
- 1958

Let (~ be a separable locally compact group. Continuing the convent ion adopted in our papers [11] and [12] we shall abbreviate the term "cont inuous un i ta ry representat ion of (~" to "representat… Expand

Borel structure in groups and their duals

- Mathematics
- 1957

Introduction. In the past decade or so much work has been done toward extending the classical theory of finite dimensional representations of compact groups to a theory of (not necessarily finite… Expand

INDUCED REPRESENTATIONS OF LOCALLY COMPACT GROUPS I

- Mathematics
- 1952

In the theory of representations of a finite group by linear transformations the closely related notions of "imprimitivity" and of "induced representation" play a prominent role. In [18] the author… Expand