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Invariant Probability Measures on Compact Right Topological Groups

In: Probability Measures on Groups X

Author

Listed:
  • Paul Milnes

    (University of Western Ontario)

Abstract

On an example of a compact right topological group, we construct a probability measure that is invariant under all right translations, is unique as such, and is also invariant under all continuous left translations. The construction is done in such a way as to indicate how to construct such a measure in the general case, starting from the structure theorem for compact right topological groups. The details for the general case are given in [4, 2, 3]. The measure on the example is also uniquely determined by invariance under all continuous left translations, a conclusion known not to be valid in general.

Suggested Citation

  • Paul Milnes, 1991. "Invariant Probability Measures on Compact Right Topological Groups," Springer Books, in: Herbert Heyer (ed.), Probability Measures on Groups X, pages 299-302, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4899-2364-6_22
    DOI: 10.1007/978-1-4899-2364-6_22
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