Abstract
We provide a new representation of an [Formula: see text]-tree by using a special set of metric rays. We have captured the four-point condition from these metric rays and shown an equivalence between the [Formula: see text]-trees with radial and river metrics, and these sets of metric rays. In stochastic analysis, these graphical representation theorems are of particular interest in identifying Brownian motions indexed by [Formula: see text]-trees.
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