Summary
This paper continues [2]. We show that the sets of infinitely divisible elements of the Delphic semigroups ℛ+ (of positive renewal sequences) and P (of standard p-functions) are additively convex, and do a Choquet analysis in each case. We draw up the “(M, m) diagram” for members of ℘, and deduce from it that the product topology on ℘ is metrizable. Finally we look at the arithmetic of ℘, showing that the simples are residual in it, and partially identifying “I 0”, the set of infinitely divisible elements without simple factors. Many examples are given.
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I am indebted to Professor D. G. Kendall for his constant help and encouragement in the course of the research leading to this paper and [2].
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Davidson, R. Arithmetic and other properties of certain Delphic semigroups. II. Z. Wahrscheinlichkeitstheorie verw Gebiete 10, 146–172 (1968). https://doi.org/10.1007/BF00531846
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DOI: https://doi.org/10.1007/BF00531846