Abstract
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 Savare proved that these two approaches are in some sense equivalent within 1 < p < infinity. 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. (C) 2021 Elsevier Inc. All rights reserved.