Plans on measures and AM-modulus

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