Hostname: page-component-cd9895bd7-fscjk Total loading time: 0 Render date: 2024-12-26T05:34:51.489Z Has data issue: false hasContentIssue false
  • English
  • Français

Nilpotent measures on compact semigroups

Published online by Cambridge University Press:  17 April 2009

H.L. Chow
H.L. Chow
Affiliation:
Department of Mathematics, Chung Chi College, The Chinese University of Hong Kong, Hong Kong.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Let S be a compact semigroup and P(S) the set of probability measures on S. Suppose P(S) has zero θ and define a measure μ ε P(S) nilpotent if μn → θ. It is shown that any measure with support containing that of θ is nilpotent, and the set of nilpotent measures is convex and dense in P(S). A measure μ is called mean-nilpotent if (μ + μ2 + … + μn)/n → θ, and can be characterized in terms of its support.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 12 , Issue 1 , February 1975 , pp. 149 - 153
Copyright
Copyright © Australian Mathematical Society 1975

References

[1]Chow, H.L., “On supports of semigroups of measures”, Proc. Edinburgh Math. Soc. (2) 19 (1974), 31–33.CrossRefGoogle Scholar
[2]Chow, H.L., “Quasi-nilpotent sets in semigroups”, Proc. Amer. Math. Soc. (to appear).Google Scholar
[3]Glicksberg, Irving, “Convolution semigroups of measures”, Pacific J. Math. 9 (1959), 51–67.CrossRefGoogle Scholar
[4]Miranda, A.B. Paalman-de, Topological semigroups, 2nd ed. (Mathematical Centre Tracts, 11. Mathematisch Centrum, Amsterdam, 1970).Google Scholar
[5]Schwarz, Štefan, “Convolution semigroup of measures on compact non-commutative semigroups”, Czechoslovak Math. J. 14 (89) (1964), 95–115.CrossRefGoogle Scholar
[6]Wendel, J.G., “Haar measure and the semigroup of measures on a compact group”, Proc. Amer. Math. Soc. 5 (1954), 923–929.CrossRefGoogle Scholar