For measuring families of curves, or, more generally, of measures, $M_p$-modulus is traditionally used. More recent studies use so-called plans on measures. In their fundamental paper [6], Ambrosio, Di Marino and Savaré proved that these two approaches are in some sense equivalent within $1<p<\infty$. We consider the limiting case $p=1$ and show that the AM-modulus can be obtained alternatively by the plan approach. On the way, we demonstrate unexpected behavior of the AM-modulus in comparison with usual capacities and consider the relations between the $M_1$–modulus and the AM–modulus.

中文翻译：

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措施计划和 AM 模量

为了测量曲线族，或者更一般地说，测量的是， ${米}_{磷}$-modulus 传统上使用。最近的研究使用所谓的措施计划。在他们的基础论文 [6] 中，Ambrosio、Di Marino 和 Savaré 证明了这两种方法在某种意义上是等价的。$1<磷<\infty$. 我们考虑极限情况$磷=1$并表明可以通过计划方法替代地获得AM模量。在此过程中，我们展示了AM模量与通常容量相比的意外行为，并考虑了${米}_1$-模量和AM -模量。