Representation Theorems of $\mathbb{R}$-trees and Brownian Motions Indexed by $\mathbb{R}$-trees

Asuman G. Aksoy, Monariah Al-Ansari, Qidi Peng

We provide a new representation of an $\mathbb{R}$-tree by using a special set of metric rays. We have captured the four-point condition from these metric rays and shown an equivale…