Motivated by the work of Lovász and Szegedy on the convergence and limits of dense graph sequences [10], we investigate the convergence and limits of finite trees with respect to sampling in normalized distance. We introduce dendrons (a notion based on separable real trees) and show that the sampling limits of finite trees are exactly the dendrons. We also prove that the limit dendron is unique.

中文翻译：

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有限树的收敛与极限

受 Lovász 和 Szegedy 关于稠密图序列收敛和极限的工作的启发 [10]，我们研究了有限树在归一化距离采样方面的收敛和极限。我们引入了树突（一种基于可分离实树的概念）并表明有限树的采样限制正是树突。我们还证明了极限树突是唯一的。