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A remark on groups with the fixed point property


Author: Barry Simon
Journal: Proc. Amer. Math. Soc. 32 (1972), 623-624
MSC: Primary 22D40
DOI: https://doi.org/10.1090/S0002-9939-1972-0301138-2
MathSciNet review: 0301138
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Abstract: We prove that any group with the fixed point property actually leaves fixed points for measurable actions rather than only jointly continuous actions.


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

  • [1] G. Choquet, Lectures on analysis, Benjamin, New York, 1968.
  • [2] M. Day, Fixed-point theorems for compact convex sets, Illinois J. Math. 5 (1961), 585-590; Correction, ibid. 8 (1964), 713. MR 25 #1547. MR 0138100 (25:1547)
  • [3] F. P. Greenleaf, Invariant means on topological groups and their applications, Van Nostrand Math. Studies, no 16, Van Nostrand, New York, 1969. MR 40 #4776. MR 0251549 (40:4776)
  • [4] N. Rickert, Amenable groups and groups with the fixed point property, Trans. Amer. Math. Soc. 127 (1967), 221-232. MR 36 #5260. MR 0222208 (36:5260)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1972-0301138-2
Keywords: Fixed point property, amenable group
Article copyright: © Copyright 1972 American Mathematical Society

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