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Right invariant integrals on locally compact semigroups

Published online by Cambridge University Press:  09 April 2009

J. H. Michael
J. H. Michael
Affiliation:
University of Adelaide, South Australia.
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An integral on a locally compact Hausdorff semigroup ς is a non-trivial, positive, linear functional μ on the space of continuous real-valued functions on ς with compact supports. If ς has the property: (A) for each pair of compact sets C, D of S, the set is compact; then, whenever and a ∈ S, the function fa defined by is also in . An integral μ on a locally compact semigroup S with the property (A) is said to be right invariant if for all j ∈ and all a ∈ S.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 4 , Issue 3 , August 1964 , pp. 273 - 286
Copyright
Copyright © Australian Mathematical Society 1964

References

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