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Uniqueness results for groups of measure preserving transformations

Author: Robert R. Kallman
Journal: Proc. Amer. Math. Soc. 95 (1985), 87-90
MSC: Primary 28D15; Secondary 22A05
MathSciNet review: 796452
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Abstract: Let $ G$ be the group of measurable, invertible, measure preserving transformations either of the unit inverval or of the line. Then $ G$ has a unique topology in which it is a complete separable metric group.

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

  • [1] R. J. Aumann, Random measure preserving transformations, Proc. Fifth Berkeley Symposium on Mathematical Statistics and Probability, Vol. 2, Part 2, Univ. of California Press, Berekeley, Calif., 1967, pp. 321-326. MR 0222247 (36:5299)
  • [2] K. Kuratowski, Topology. Vol. I, Academic Press, New York, 1966. MR 0217751 (36:840)
  • [3] G. W. Mackey, Borel structures in groups and their duals, Trans. Amer. Math. Soc. 85 (1957), 134-165. MR 0089999 (19:752b)

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