# Lebesgue Measure Preserving Thompson's Monoid

@article{Li2020LebesgueMP, title={Lebesgue Measure Preserving Thompson's Monoid}, author={William Li}, journal={arXiv: Dynamical Systems}, year={2020} }

This paper defines Lebesgue measure preserving Thompson's monoid, denoted by $\mathbb{G}$, which is modeled on Thompson's group $\mathbb{F}$ except that the elements of $\mathbb{G}$ are non-invertible. Moreover, it is required that the elements of $\mathbb{G}$ preserve Lebesgue measure. Monoid $\mathbb{G}$ exhibits very different properties from Thompson's group $\mathbb{F}$. The paper studies a number of algebraic (group-theoretic) and dynamical properties of $\mathbb{G}$ including…

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