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On certain conjectures on invariant measures on semigroups

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Abstract

A conjecture stating that a locally compact semigroup admits a twosided semi-invariant measure iff it contains a kernel which is a unimodular group, is proven. Also a conjecture stating that the support of an r*-invariant measure is a left group, is proven under the condition that for some a ε F (=support of the measure), aF is right cancellative. Moreover four types of invariance for regular probability measures are shown to be equivalent. Also a new proof of the equivalence of a two-sided semi-invariant probability measure and the existence of a kernel which is a compact group, is given.

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References

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Authors and Affiliations

  1. University of South Florida, 33620, Tampa, Florida

    N. A. Tserpes & A. Mukherjea

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  1. N. A. Tserpes
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  2. A. Mukherjea
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Communicated by K. H. Hofmann

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Tserpes, N.A., Mukherjea, A. On certain conjectures on invariant measures on semigroups. Semigroup Forum 1, 260–266 (1970). https://doi.org/10.1007/BF02573045

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  • DOI: https://doi.org/10.1007/BF02573045

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