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Proceedings of the American Mathematical Society

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Translation invariant sigma algebras on groups

Author: D. A. Lind
Journal: Proc. Amer. Math. Soc. 42 (1974), 218-221
MSC: Primary 28A65; Secondary 22D40
MathSciNet review: 0325924
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Abstract: The translation invariant sigma subalgebras of the Baire sets of a locally compact abelian group are characterized as those periodic under some closed subgroup.

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

  • [1] R. L. Adler, Invariant and reducing subalgebras of measure preserving transformations, Trans. Amer. Math. Soc. 110 (1964), 350-360. MR 28 #183. MR 0156941 (28:183)
  • [2] P. R. Halmos, Measure theory, Van Nostrand, Princeton, N.J., 1950. MR 11, 504. MR 0033869 (11:504d)
  • [3] A. Ionescu Tulcea and C. Ionescu Tulcea, On the existence of a lifting commuting with the left translations of an arbitrary locally compact group, Proc. Fifth Berkeley Sympos. Math. Statist. and Probability (Berkeley, Calif., 1965/66), Vol. II, Contributions to Probability Theory, part 1, Univ. of California Press, Berkeley, Calif., 1967, pp. 63-97. MR 35 #2997. MR 0212122 (35:2997)
  • [4] V. A. Rohlin, A ``general'' measure-preserving transformation is not mixing, Dokl. Akad. Nauk SSSR 60 (1948), 349-351. (Russian) MR 9, 504. MR 0024503 (9:504d)

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Keywords: Translation invariant sigma algebras, closed subgroup, periodic Baire sets, Stone-Weierstrass theorem
Article copyright: © Copyright 1974 American Mathematical Society

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