A model of irrigation network, where lower branches must be thicker in order to support the weight of the higher ones, was recently introduced in [7]. This leads to a countable family of ODEs, describing the thickness of every branch, solved by backward induction. The present paper determines what kind of measures can be irrigated with a finite weighted cost. Indeed, the boundedness of the cost depends on the dimension of the support of the irrigated measure, and also on the asymptotic properties of the ODE which determines the thickness of branches.

中文翻译：

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加权灌溉计划的灌溉措施

灌溉网络模型，其中较低的分支必须更粗以支撑较高分支的重量，最近在 [7]。这导致了一个可数的 ODE 族，描述了每个分支的厚度，通过向后归纳来解决。本文确定了可以使用有限加权成本灌溉的措施。实际上，成本的有界性取决于灌溉措施的支持维度，还取决于决定分支粗细的 ODE 的渐近特性。