Ergodic theory and virtual groups

@article{Mackey1966ErgodicTA,
  title={Ergodic theory and virtual groups},
  author={G. Mackey},
  journal={Mathematische Annalen},
  year={1966},
  volume={166},
  pages={187-207}
}
  • G. Mackey
  • Published 1966
  • Mathematics
  • Mathematische Annalen
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References

SHOWING 1-10 OF 12 REFERENCES
Transformation Groups and C ∗ -algebras
ERGODIC THEORY, GROUP THEORY AND DIFFERENTIAL GEOMETRY.
  • G. Mackey
  • 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: InterscienceExpand
On invariant measures
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 inExpand
Unitary representations of group extensions. I
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 "representatExpand
Borel structure in groups and their duals
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 finiteExpand
INDUCED REPRESENTATIONS OF LOCALLY COMPACT GROUPS I
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 authorExpand
L'integration dans les groupes topologiques et ses applications
  • A. Weil
  • Mathematics, Computer Science
  • 1951
...
1
2
...