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Generating dense subgroups of measure preserving transformations


Author: V. S. Prasad
Journal: Proc. Amer. Math. Soc. 83 (1981), 286-288
MSC: Primary 28D05
DOI: https://doi.org/10.1090/S0002-9939-1981-0624915-2
MathSciNet review: 624915
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Abstract: Except for a set of first category, all pairs of measure preserving transformations generate a dense subgroup of $ G$, the group of all invertible measure preserving transformations of the unit interval when $ G$ has the weak topology.


References [Enhancements On Off] (What's this?)

  • [1] R. Grzaślewicz, Density theorems for measurable transformations (preprint).
  • [2] P. R. Halmos, Lectures on ergodic theory, Chelsea, New York, 1956. MR 0097489 (20:3958)
  • [3] J. Schreier and S. Ulam, Sur le nombre des générateurs d'un groupe topologique compact et connexe, Fund. Math. 24 (1935), 302-304.

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1981-0624915-2
Keywords: Measure preserving transformation, weak topology, cyclic dyadic permutation
Article copyright: © Copyright 1981 American Mathematical Society

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