This paper defines the Lebesgue measure preserving Thompson monoid, denoted by G, which is modeled on the Thompson group F except that the elements of G preserve the Lebesgue measure and can be non-invertible. The paper shows that any element of the monoid G is the composition of a finite number of basic elements of the monoid G and the generators of the Thompson group F. However, unlike the Thompson group F, the monoid G is not finitely generated. The paper then defines equivalence classes of the monoid G, use them to construct a monoid H that is finitely generated, and shows that the union of the elements of the monoid H is a set of equivalence classes, the union of which is G.
"Lebesgue Measure Preserving Thompson Monoid and Its Properties of Decomposition and Generators,"
Rose-Hulman Undergraduate Mathematics Journal: Vol. 22:
1, Article 8.
Available at: https://scholar.rose-hulman.edu/rhumj/vol22/iss1/8
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