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Semigroups in Probability Theory

In: Probability Measures on Groups X

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  • Paul Ressel

    (Katholische Universität Eichstätt)

Abstract

Semigroups are very natural and general structures and enter our mathematical life from the very beginning (N with respect to addition, multiplication, maximum or minimum, sets with respect to union or intersection). Due to their simple axioms they are very often and easily found. If M is a nonempty set and S = M M is the set of all mappings from M to M, then S is a semigroup with respect to composition, and in fact every semigroup can be realized as a subsemi-group of M M for some M.

Suggested Citation

  • Paul Ressel, 1991. "Semigroups in Probability Theory," Springer Books, in: Herbert Heyer (ed.), Probability Measures on Groups X, pages 337-363, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4899-2364-6_26
    DOI: 10.1007/978-1-4899-2364-6_26
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