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.
KeywordsPoint Process Random Measure Positive Definite Matrix Positive Definiteness Neutral Element
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