Invariant Radon measures and minimal sets for subgroups of ${\text{Homeo}}_{+}(\mathbb{R})$

Hui Xu, Enhui Shi, Yiruo Wang

Let $G$ be a subgroup of ${\text{Homeo}}_{+}(\mathbb{R})$ without crossed elements. We show the equivalence among three items: (1) existence of $G$-invariant Radon measures on $\mathbb…