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.

Author Bio

William Li is a rising freshman at Stanford University where he hopes to study symbolic systems. Will is a passionate math/CS researcher who works to promote science education and lead STEM outreach in underrepresented communities. Outside of science, Will is a nationally acclaimed debater who enjoys promoting tech policy.