Hostname: page-component-586b7cd67f-t8hqh Total loading time: 0 Render date: 2024-11-25T07:04:30.307Z Has data issue: false hasContentIssue false

Left invariant measure in topological semigroups

Published online by Cambridge University Press:  09 April 2009

James Chew
Affiliation:
Michigan State University, E. Lansing, Michigan, U.S.A. Haile Sellassie I University, Addis Ababa, Ethiopia
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.

We consider the problem of the existence of a left invariant measure in a class of topological semigroups. Several authors have considered this and related problems on semigroups satisfying similar conditions, but the invariance they considered is right invariance. This paper is different in that it deals with left invariance.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1975

References

Argabright, L. N. (1966), ‘A note on invariant integrals on locally compact semigroups’, Proc. Amer. Math. Soc. 17, 377382.CrossRefGoogle Scholar
Argabright, L. N. (1966a), ‘Invariant means on topological semigroups’, Pacific J. Math. 16, 193203.CrossRefGoogle Scholar
Clifford, A. H. and Preston, G. B. (1961), The Algebraic Theory of Semigroups, vol. I (Mathematical Surveys, Amer. Math. Soc., 1961).Google Scholar
Doyle, and Warne, (1963), ‘Some properties of groupoids’, Amer. Math. Monthly 70, 10511057.CrossRefGoogle Scholar
Ellis, R. (1957), ‘A note on the continuity of the inverse’, Proc. Amer. Math. Soc. 8, 372373.CrossRefGoogle Scholar
Halmos, P. (1950), Measure Theory (Van Nostrand, Princeton, N.J. 1950).CrossRefGoogle Scholar
Kelley, J. L. (1955), General Topology (Van Nostrand, Princeton, N.J., 1955).Google Scholar
Michael, J. H. (1964), ‘Right invariant integrals on locally compact semigroups’, J. Austral. Math. Soc. 4, 273286.CrossRefGoogle Scholar
Mostert, P. S., (1964), ‘Comments on the preceding paper of Michael’, J. Austral. Math. Soc. 4, 287288.CrossRefGoogle Scholar
Problem 5335 (1966), ‘A closed set of idempotents’, Amer. Math. Monthly 73, 1025.Google Scholar