A real tree is a metric space in which any two points are joined by a unique arc and that arc is isometric to a real interval of length equal to their distance. Thus it is a geodesic space with no alternative route around a cycle. An ordinary finite tree with each edge replaced by an interval is an example. The Brownian continuum random tree is a random compact real tree carrying a probability measure.
Real Tree
See also
Brownian Continuum Random Tree, Metric Space, TreeExplore with Wolfram|Alpha
References
Le Gall, J.-F. "Random Trees and Applications." Probab. Surv. 2, 245-311, 2005. https://doi.org/10.1214/154957805100000140.Cite this as:
Weisstein, Eric W. "Real Tree." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/RealTree.html