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A simple proof of a covering property of locally compact groups

Authors: P. Milnes and J. V. Bondar
Journal: Proc. Amer. Math. Soc. 73 (1979), 117-118
MSC: Primary 43A07; Secondary 22D05
MathSciNet review: 512070
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Abstract: We give a simple proof of the following result of Emerson and Greenleaf.

Theorem. Let V be a relatively compact subset with nonvoid interior of a locally compact group G. Then there exist a subset $ T \subset G$ and a natural number M such that $ G = { \cup _{t \in T}}tV$ and at most M of the tV's, $ t \in T$, intersect.

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

  • [1] J. V. Bondar and P. Milnes, A survey of Hunt-Stein and related conditions on groups (submitted).
  • [2] W. R. Emerson, Ratio properties in locally compact groups, Trans. Amer. Math. Soc. 133 (1968), 179-204. MR 0237706 (38:5987)
  • [3] -, Letter to the first-named author, January 1978.
  • [4] W. R. Emerson and F. P. Greenleaf, Covering properties and Fólner conditions for locally compact groups, Math. Z. 102 (1967), 370-384. MR 0220860 (36:3912)
  • [5] P. Eymard, Initiation à la théorie des groupes moyennables, Analyse Harmonique sur les Groupes de Lie, Eymard et al., eds., Lecture Notes in Math., vol. 497, Springer-Verlag, Berlin, 1975, pp. 89-107. MR 0394037 (52:14843)
  • [6] F. P. Greenleaf, Invariant means on topological groups, Van Nostrand Math. Studies Series, no. 16, Van Nostrand, New York, 1969. MR 0251549 (40:4776)
  • [7] H. Reiter, Classical harmonic analysis and locally compact groups, Oxford Univ. Press, Cambridge, 1968. MR 0306811 (46:5933)
  • [8] M. Stone and R. von Randow, Statistically inspired conditions on the group structure of invariant experiments . . . , Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 10 (1968), 70-80. MR 0233449 (38:1771)

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Keywords: Locally compact group, amenability, covering property
Article copyright: © Copyright 1979 American Mathematical Society

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