## 186 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…

COHERENT EXTENSION OF PARTIAL AUTOMORPHISMS, FREE AMALGAMATION AND AUTOMORPHISM GROUPS

- MathematicsThe 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…

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…

ON A STRENGTHENING OF THE HERWIG – LASCAR EXTENSION THEOREM

- Mathematics
- 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…

Sur les espaces mesures singuliers I - Etude metrique-mesuree

- Mathematics
- 2004

Recall Jones-Schmidt theorem that an ergodic measured equivalence relation is strongly ergodic if and only if it has no nontrivial amenable quotient. We give two new characterizations of strong…

Locally compact groups appearing as ranges of cocycles of ergodic ℤ-actions

- MathematicsErgodic Theory and Dynamical Systems
- 1985

Abstract The paper contains the proof of the fact that every solvable locally compact separable group is the range of a cocycle of an ergodic automorphism. The proof is based on the theory of…

An amenable equivalence relation is generated by a single transformation

- MathematicsErgodic Theory and Dynamical Systems
- 1981

Abstract 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…

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…

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…

Quantized reduction as a tensor product

- Mathematics
- 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…

## References

SHOWING 1-10 OF 12 REFERENCES

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…

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…

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…

Point realizations of transformation groups

- Mathematics
- 1962

Now let S be a measure space as well as a G-space, and suppose that for each y the mapping x ---> [x]y preserves measurability and null sets. Then the a-Boolean algebra B of measurable sets modulo…