Regularity of the Semigroup of Regular Probability Measures on Locally Compact Hausdorff Topological Groups

M. N. N. Namboodiri ()
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M. N. N. Namboodiri: Cochin University of Science & Technology

Journal of Theoretical Probability, 2024, vol. 37, issue 4, 3202-3215

Abstract: Abstract Let G be a locally compact Hausdorff group, and let P(G) denote the class of all regular probability measures on G. It is well known that P(G) forms a semigroup under the convolution of measures. In this paper, we prove that P(G) is not algebraically regular in the sense that not every element has a generalized inverse. Additionally, we attempt to identify algebraically regular elements in some exceptional cases. Several supporting examples are provided to justify these assumptions.

Keywords: Measure; Semigroup; Convolution; 60B15 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s10959-024-01353-1

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